Appendix 5: Data Plotted in GraphsThis appendix contains in tabular form the data which is plotted in some of the graphs contained in Chapters 2 through 6. The number of each table corresponds to the number of the graph (in some cases the data in a table is plotted in two consecutive graphs).
Table 2.2.1
Results for internal energy and specific heat for Ising 2d square spin model, Glauber dynamics
Numbers of samples: 4000 for 32x32, 1000 for 64x64 and 100x100,
twice that number for the runs at the critical temperature for 32x32 and 64x64.
Internal energy
critical temp.
Size\T
1.00
1.50
2.00
2.27
2.50
3.00
3.50
4.00
4.50
5.00
32x32
-1.997
-1.951
-1.746
-1.434
-1.107
-0.817
-0.660
-0.557
-0.484
-0.428
64x64
-1.997
-1.951
-1.746
-1.431
-1.106
-0.817
-0.661
-0.557
-0.484
-0.428
100x100
-1.746
-1.431
-1.106
Specific heat (final 10% of timesteps)
Size\T
1.00
1.50
2.00
2.27
2.50
3.00
3.50
4.00
4.50
5.00
32x32
0.023
0.199
0.725
1.852
0.887
0.403
0.248
0.173
0.126
0.098
64x64
0.023
0.197
0.730
2.031
0.860
0.405
0.249
0.171
0.125
0.097
100x100
0.727
2.102
0.887
Table 2.3.1
Internal energy and specific heat for Ising 2d square model, Swendsen-Wang dynamics
Temperature
1.00
1.50
2.00
2.27
2.50
3.00
3.50
4.00
4.50
5.00
Sw-Wang prob.
0.8647
0.7364
0.6321
0.5858
0.5507
0.4866
0.4353
0.3935
0.3588
0.3297
Largest timepoint
100
1000
1000
1000
200
200
200
200
200
200
No. of samples
1000
1000
1000
2000
1000
1000
1000
1000
1000
1000
Internal energy
critical temp.
64x64
-1.997
-1.951
-1.746
-1.424
-1.106
-0.817
-0.659
-0.558
-0.483
-0.429
Specific heat (final 10% of timesteps)
64x64
0.025
0.197
0.730
2.190
0.881
0.408
0.254
0.174
0.126
0.101
Internal energy and specific heat for Ising 2d square model, Wolff dynamics
Temperature
1.00
1.50
2.00
2.27
2.50
3.00
3.50
4.00
4.50
5.00
Wolff prob.
0.8647
0.7364
0.6321
0.5858
0.5507
0.4866
0.4353
0.3935
0.3588
0.3297
Largest timepoint
250
250
250
250
250
250
250
250
250
250
No. of samples
1000
1000
1000
1000
1000
1000
1000
500
500
500
Internal energy
critical temp.
64x64
-1.997
-1.951
-1.745
-1.434
-1.113
-0.819
-0.661
-0.558
-0.484
-0.429
Specific heat (final 10% of timesteps)
64x64
0.023
0.197
0.738
1.937
0.885
0.402
0.253
0.169
0.126
0.098
Table 3.3.1
Determination of critical temperature for Ising square model using Binder cumulant
1000 samples, Wolff dynamics, averaged over last 40% of 80 timepoints.
Mean
Latttice size
Std. dev.
Latttice size
Temperature
60
100
150
60
100
150
2.200
0.6611
0.6645
0.6657
0.0004
0.0001
0.0001
2.240
0.6489
0.6569
0.6616
0.0012
0.0007
0.0004
2.250
0.6428
0.6517
0.6577
0.0017
0.0009
0.0007
2.260
0.6356
0.6427
0.6488
0.0020
0.0012
0.0015
2.270
0.6255
0.6291
0.6307
0.0022
0.0018
0.0020
2.280
0.6162
0.6074
0.5926
0.0027
0.0040
0.0034
2.290
0.5999
0.5739
0.5297
0.0026
0.0043
0.0056
2.300
0.5803
0.5268
0.4305
0.0043
0.0071
0.0096
2.325
0.5137
0.3685
0.1975
0.0077
0.0148
0.0225
2.350
0.4229
0.2167
0.0828
0.0090
0.0186
0.0353
Table 3.3.2
Determination of critical temperature for Ising triangular model using Binder cumulant
Swendsen-Wang dynamics, max timepoint = 80
1000 samples, averaged over last 50% (40 timepoints)
Mean
Latttice size
Std.dev.
Temperature
20
40
60
20
40
60
3.500
0.6493
0.6594
0.6631
0.0014
0.0006
0.0003
3.550
0.6402
0.6525
0.6586
0.0020
0.0010
0.0007
3.575
0.6332
0.6466
0.6541
0.0026
0.0011
0.0008
3.600
0.6277
0.6387
0.6447
0.0021
0.0014
0.0017
3.620
0.6197
0.6273
0.6332
0.0023
0.0019
0.0018
3.630
0.6177
0.6218
0.6236
0.0025
0.0031
0.0028
3.640
0.6141
0.6126
0.6138
0.0028
0.0032
0.0024
3.645
0.6110
0.6090
0.6066
0.0037
0.0037
0.0037
3.650
0.6066
0.6035
0.5991
0.0035
0.0031
0.0042
3.660
0.6034
0.5933
0.5857
0.0032
0.0042
0.0042
3.670
0.5815
0.5392
0.4904
0.0037
0.0082
0.0082
3.800
0.5082
0.3501
0.2107
0.0074
0.0155
0.0180
Table 3.3.3
Determination of critical temperature for Ising honeycomb model using Binder cumulant
Swendsen-Wang dynamics
1000 samples, averaged over last 50% of 80 timepoints.
Mean
Latttice size
Standard deviations
Temperature
20
40
60
20
40
60
1.500
0.6168
0.6302
0.6402
0.0029
0.0037
0.0014
1.505
0.6126
0.6242
0.6325
0.0031
0.0029
0.0030
1.510
0.6092
0.6162
0.6230
0.0025
0.0021
0.0028
1.515
0.6022
0.6046
0.6112
0.0030
0.0037
0.0036
1.520
0.5986
0.5937
0.5968
0.0044
0.0035
0.0033
1.525
0.5911
0.5855
0.5704
0.0037
0.0041
0.0043
1.530
0.5815
0.5686
0.5499
0.0054
0.0048
0.0046
Table 3.4.5
Determination of critical temperature for Ising cubic model using Binder cumulant (Wolff dynamics)
1000 samples, averaged over last 50% of 81 timeslices (40 timeslices)
Mean
Std. dev.
Temperature
8
12
16
8
12
16
4.40
0.6117
0.6338
0.6480
0.0033
0.0013
0.0008
4.46
0.5932
0.6097
0.6238
0.0040
0.0029
0.0021
4.48
0.5855
0.5987
0.6098
0.0043
0.0032
0.0023
4.49
0.5817
0.5933
0.6006
0.0058
0.0033
0.0036
4.50
0.5779
0.5849
0.5911
0.0047
0.0040
0.0035
4.51
0.5752
0.5787
0.5791
0.0044
0.0039
0.0041
4.52
0.5701
0.5676
0.5648
0.0051
0.0049
0.0035
4.54
0.5602
0.5508
0.5366
0.0040
0.0058
0.0071
4.56
0.5509
0.5308
0.5019
0.0051
0.0062
0.0072
4.60
0.5305
0.4835
0.4185
0.0060
0.0081
0.0108
Table 3.4.6
Determination of critical temperature for Ising diamond model using Binder cumulant (Wolff dynamics)
1000 samples, averaged over last 50% of 81 timeslices (40 timeslices)
Mean
Std. dev.
Temperature
8
12
16
8
12
16
2.600
0.6209
0.6472
0.6573
0.0022
0.0011
0.0005
2.650
0.5982
0.6239
0.6411
0.0037
0.0024
0.0010
2.675
0.5846
0.6039
0.6194
0.0036
0.0034
0.0026
2.700
0.5662
0.5724
0.5760
0.0049
0.0051
0.0041
2.725
0.5447
0.5302
0.5109
0.0040
0.0057
0.0064
2.750
0.5231
0.4833
0.4269
0.0065
0.0071
0.0115
2.800
0.4701
0.3677
0.2540
0.0081
0.0112
0.0238
Table 3.5.1
Determination of critical temperature for Ising 4d hypercubic model using Binder cumulant (Wolff dynamics)
1000 samples, averaged over last 50% of 81 timeslices (40 timeslices)
Mean
Std. dev.
Temperature
6
8
10
6
8
10
6.30
0.6449
0.6588
0.6632
0.0011
0.0003
0.0002
6.50
0.6095
0.6379
0.6520
0.0028
0.0011
0.0008
6.60
0.5741
0.5981
0.6192
0.0040
0.0030
0.0021
6.65
0.5491
0.5600
0.5753
0.0053
0.0050
0.0047
6.70
0.5205
0.5128
0.5052
0.0065
0.0076
0.0067
6.75
0.4881
0.4609
0.4156
0.0086
0.0102
0.0091
6.80
0.4562
0.3975
0.3209
0.0100
0.0132
0.0168
6.85
0.4188
0.3359
0.2406
0.0076
0.0162
0.0227
6.90
0.3849
0.2758
0.1704
0.0152
0.0186
0.0231
7.00
0.3110
0.1793
0.0739
0.0159
0.0323
0.0342
Table 3.5.2
Determination of critical temperature for Ising 4d hypercubic model using Binder cumulant
Wolff dynamics
4000 samples, averaged over last 50% of 81 timeslices (40 timeslices)
Mean
Std. dev.
Temperature
6
8
10
6
8
10
6.63
0.5586
0.5776
0.5968
0.0027
0.0022
0.0017
6.65
0.5483
0.5617
0.5762
0.0025
0.0021
0.0020
6.67
0.5387
0.5446
0.5515
0.0032
0.0031
0.0028
6.69
0.5260
0.5255
0.5212
0.0034
0.0034
0.0041
6.71
0.5141
0.5041
0.4891
0.0039
0.0032
0.0035
6.73
0.5019
0.4831
0.4531
0.0032
0.0047
0.0052
Table 4.2.1
Determination of critical temperature for site-diluted (p = 0.8) Ising cubic model
using Binder cumulant (lattice sizes 10, 20 and 30, 2000 samples each)
Wolff dynamics, max timepoint = 80, averaged over last 40% (32 timepoints).
Size 10
Temperature
Magnetiz'n
Binder cum.
Std.dev.
3.485
0.4334
0.5756
0.0030
3.490
0.4212
0.5671
0.0037
3.495
0.4197
0.5652
0.0031
3.500
0.4193
0.5670
0.0041
3.505
0.4165
0.5659
0.0036
3.510
0.4059
0.5564
0.0039
Size 20
Temperature
Mag'n
Binder cum.
Std.dev.
3.485
0.3299
0.5894
0.0023
3.490
0.3142
0.5783
0.0032
3.495
0.3045
0.5708
0.0036
3.500
0.2991
0.5661
0.0030
3.505
0.2914
0.5597
0.0038
3.510
0.2749
0.5422
0.0031
Size 30
Temperature
Mag'n
Binder cum.
Std.dev.
3.485
0.2889
0.6050
0.0021
3.490
0.2717
0.5923
0.0028
3.495
0.2601
0.5806
0.0028
3.500
0.2416
0.5650
0.0033
3.505
0.2293
0.5489
0.0036
3.510
0.2157
0.5326
0.0051
Table 4.3.5
Determination of critical temperatures for a range of site dilutions
with the 2d squre Ising model using Swendsen-Wang and Wolf dynamics
and sample sizes from 500 to 60,000.
*********************
***************
**************
***************
p=0.900 (Wolff, 1000 samples)
Mean of Binder cumulant
Standard deviation
Size
20
30
40
20
30
40
Temp
1.82
0.6477
0.6532
0.6578
0.0014
0.0010
0.0006
1.84
0.6432
0.6484
0.6538
0.0016
0.0015
0.0010
1.86
0.6383
0.6435
0.6465
0.0017
0.0019
0.0014
1.90
0.6217
0.6206
0.6238
0.0023
0.0032
0.0025
1.91
0.6201
0.6159
0.6205
0.0026
0.0034
0.0033
1.92
0.6137
0.6138
0.6165
0.0031
0.0030
0.0030
1.93
0.6080
0.6081
0.6050
0.0032
0.0027
0.0033
1.94
0.6040
0.5983
0.5952
0.0030
0.0037
0.0039
1.95
0.5979
0.5940
0.5884
0.0036
0.0036
0.0035
1.96
0.5930
0.5887
0.5767
0.0046
0.0039
0.0040
1.97
0.5923
0.5833
0.5612
0.0037
0.0033
0.0062
1.98
0.5857
0.5725
0.5409
0.0034
0.0052
0.0057
1.99
0.5791
0.5585
0.5270
0.0038
0.0056
0.0059
2.00
0.5749
0.5572
0.5207
0.0043
0.0065
0.0065
*********************
***************
**************
***************
p=0.837 (Sw-W, 500 samples)
Size
20
30
60
20
30
60
Temp
1.00
0.6665
0.6665
0.6666
0.0000
0.0000
0.0000
1.20
0.6659
0.6662
0.6666
0.0001
0.0001
0.0000
1.40
0.6632
0.6648
0.6661
0.0004
0.0003
0.0001
1.54
0.6535
0.6581
0.6635
0.0018
0.0010
0.0003
1.57
0.6478
0.6548
0.6614
0.0016
0.0015
0.0006
1.60
0.6415
0.6481
0.6552
0.0026
0.0021
0.0012
1.63
0.6302
0.6381
0.6435
0.0030
0.0022
0.0020
1.66
0.6101
0.6207
0.6127
0.0039
0.0039
0.0044
1.80
0.5031
0.4204
0.2279
0.0126
0.0131
0.0306
2.00
0.2876
0.1595
0.0381
0.0284
0.0372
0.0529
*********************
***************
**************
***************
p=0.800 (Wolff, 2000 samples)
Size
20
30
40
20
30
40
Temp
1.44
0.6459
0.6498
0.6528
0.0010
0.0008
0.0008
1.46
0.6406
0.6442
0.6492
0.0015
0.0013
0.0009
1.48
0.6343
0.6375
0.6387
0.0015
0.0017
0.0017
1.49
0.6259
0.6334
0.6331
0.0017
0.0016
0.0016
1.50
0.6287
0.6296
0.6288
0.0018
0.0020
0.0014
1.51
0.6241
0.6264
0.6266
0.0020
0.0019
0.0018
1.52
0.6224
0.6184
0.6181
0.0015
0.0023
0.0020
1.54
0.6099
0.6071
0.6054
0.0025
0.0026
0.0028
1.56
0.6056
0.5968
0.5888
0.0029
0.0029
0.0034
*********************
***************
**************
***************
p=0.756 (Sw-W, 1000 samples)
Size
20
30
60
20
30
60
Temp
1.200
0.6507
0.6579
0.6629
0.0018
0.0013
0.0005
1.225
0.6510
0.6558
0.6615
0.0009
0.0009
0.0004
1.250
0.6413
0.6510
0.6558
0.0015
0.0015
0.0007
1.275
0.6448
0.6426
0.6518
0.0019
0.0015
0.0013
1.300
0.6392
0.6323
0.6323
0.0029
0.0028
0.0032
1.325
0.6276
0.6189
0.6214
0.0023
0.0033
0.0024
1.350
0.6219
0.6042
0.5824
0.0029
0.0035
0.0042
1.375
0.6005
0.5895
0.5326
0.0035
0.0049
0.0075
1.400
0.5942
0.5639
0.4604
0.0051
0.0075
0.0149
*********************
***************
**************
***************
p=0.725 (Wolff, 8000 samples)
Size
20
30
40
20
30
40
Temp
1.10
0.6478
0.6521
0.6551
0.0005
0.0005
0.0003
1.12
0.6443
0.6482
0.6521
0.0005
0.0005
0.0004
1.14
0.6426
0.6443
0.6437
0.0006
0.0005
0.0006
1.16
0.6350
0.6380
0.6360
0.0009
0.0007
0.0009
1.17
0.6356
0.6284
0.6337
0.0007
0.0007
0.0009
1.18
0.6296
0.6293
0.6320
0.0010
0.0009
0.0007
1.20
0.6215
0.6180
0.6164
0.0010
0.0009
0.0010
*********************
***************
**************
***************
p=0.700 (Wolff, 12000 samples)
Size
20
30
40
20
30
40
Temp
0.94
0.6542
0.6581
0.6596
0.0003
0.0002
0.0002
0.96
0.6521
0.6545
0.6574
0.0003
0.0003
0.0002
0.98
0.6503
0.6515
0.6551
0.0003
0.0004
0.0003
1.00
0.6473
0.6486
0.6519
0.0003
0.0004
0.0003
1.01
0.6459
0.6476
0.6451
0.0004
0.0004
0.0005
1.02
0.6433
0.6436
0.6429
0.0005
0.0004
0.0005
1.03
0.6378
0.6429
0.6435
0.0006
0.0005
0.0004
1.04
0.6388
0.6387
0.6408
0.0006
0.0006
0.0006
1.06
0.6339
0.6287
0.6325
0.0007
0.0004
0.0007
1.08
0.6296
0.6280
0.6205
0.0007
0.0007
0.0008
1.10
0.6185
0.6149
0.6111
0.0008
0.0007
0.0009
*********************
***************
**************
***************
p=0.680 (Wolff, 20,000 samples)
Size
20
30
40
20
30
40
Temp
0.87
0.6520
0.6535
0.6559
0.0003
0.0002
0.0002
0.89
0.6476
0.6481
0.6516
0.0003
0.0003
0.0003
0.91
0.6457
0.6497
0.6488
0.0004
0.0003
0.0003
0.93
0.6427
0.6418
0.6440
0.0003
0.0005
0.0003
0.95
0.6389
0.6367
0.6367
0.0004
0.0005
0.0004
0.97
0.6312
0.6276
0.6305
0.0005
0.0006
0.0005
0.99
0.6283
0.6176
0.6153
0.0007
0.0007
0.0006
1.01
0.6197
0.6130
0.6056
0.0007
0.0007
0.0008
1.03
0.6113
0.5997
0.5965
0.0007
0.0008
0.0009
********************
***************
**************
***************
p=0.660 (Wolff, 40,000 samples)
Size
20
30
40
20
30
40
Temp
0.82
0.6428
0.6421
0.6446
0.0003
0.0003
0.0003
0.83
0.6390
0.6399
0.6436
0.0003
0.0004
0.0003
0.84
0.6387
0.6385
0.6381
0.0003
0.0003
0.0003
0.85
0.6365
0.6368
0.6362
0.0003
0.0003
0.0003
0.86
0.6316
0.6319
0.6319
0.0004
0.0004
0.0004
0.87
0.6320
0.6282
0.6259
0.0003
0.0004
0.0004
0.88
0.6289
0.6222
0.6244
0.0003
0.0004
0.0004
0.89
0.6273
0.6195
0.6213
0.0004
0.0004
0.0005
0.90
0.6199
0.6138
0.6113
0.0003
0.0005
0.0005
*********************
***************
**************
***************
p=0.650 (Wolff, 40,000 samples)
Size
20
40
60
20
40
60
Temp
0.650
0.6535
0.6584
0.6614
0.0002
0.0001
0.0001
0.675
0.6529
0.6570
0.6594
0.0002
0.0001
0.0001
0.700
0.6511
0.6553
0.6574
0.0002
0.0002
0.0001
0.725
0.6482
0.6516
0.6546
0.0002
0.0002
0.0001
0.750
0.6451
0.6461
0.6489
0.0003
0.0002
0.0003
0.775
0.6429
0.6393
0.6439
0.0003
0.0003
0.0002
0.800
0.6353
0.6326
0.6355
0.0004
0.0004
0.0003
0.825
0.6294
0.6222
0.6214
0.0003
0.0005
0.0005
0.850
0.6222
0.6103
0.6060
0.0004
0.0004
0.0005
********************
**************
**************
***************
p=0.645 (Wolff, 40,000 samples)
Size
20
30
40
20
30
40
Temp
0.72
0.6429
0.6461
0.6472
0.0003
0.0002
0.0002
0.73
0.6426
0.6419
0.6430
0.0003
0.0003
0.0003
0.74
0.6406
0.6378
0.6405
0.0003
0.0003
0.0003
0.75
0.6395
0.6393
0.6417
0.0003
0.0003
0.0003
0.76
0.6388
0.6347
0.6364
0.0003
0.0004
0.0004
0.77
0.6338
0.6312
0.6363
0.0003
0.0003
0.0003
0.78
0.6316
0.6297
0.6322
0.0004
0.0003
0.0004
0.79
0.6288
0.6280
0.6266
0.0004
0.0003
0.0004
0.80
0.6296
0.6225
0.6213
0.0004
0.0005
0.0004
********************
**************
**************
***************
p=0.640 (Sw-W, 10,000 samples)
Size
20
30
40
20
30
40
Temp
0.450
0.6618
0.6619
0.6638
0.0001
0.0002
0.0001
0.500
0.6581
0.6609
0.6630
0.0002
0.0002
0.0001
0.525
0.6597
0.6592
0.6602
0.0002
0.0002
0.0002
0.550
0.6555
0.6589
0.6607
0.0003
0.0003
0.0002
0.575
0.6584
0.6593
0.6597
0.0002
0.0002
0.0002
0.600
0.6541
0.6551
0.6583
0.0004
0.0002
0.0003
0.625
0.6502
0.6544
0.6562
0.0003
0.0005
0.0002
0.650
0.6511
0.6482
0.6559
0.0004
0.0005
0.0003
0.675
0.6480
0.6485
0.6471
0.0004
0.0005
0.0004
0.700
0.6410
0.6436
0.6409
0.0006
0.0004
0.0006
0.750
0.6389
0.6343
0.6295
0.0006
0.0005
0.0007
********************
**************
**************
***************
p=0.625 (Wolff, 30,000 samples, averaged over last 50% of 60 timeslices, i.e., 30)
Size
20
30
40
20
30
40
Temp
0.350
0.6581
0.6558
0.6588
0.0002
0.0003
0.0004
0.400
0.6558
0.6535
0.6562
0.0003
0.0003
0.0004
0.450
0.6519
0.6538
0.6546
0.0003
0.0003
0.0005
0.475
0.6521
0.6530
0.6502
0.0003
0.0004
0.0006
0.500
0.6540
0.6476
0.6522
0.0003
0.0004
0.0005
0.525
0.6499
0.6488
0.6495
0.0003
0.0005
0.0005
0.550
0.6454
0.6461
0.6463
0.0004
0.0005
0.0006
0.600
0.6364
0.6418
0.6424
0.0003
0.0005
0.0005
********************
**************
**************
***************
p=0.610 (Wolff, 201 timeslices, average over last 25%)
Size
20
40
60
20
40
60
Samples
40000
20000
10000
Time in hours
8.55
16.20
13.10
Total computing time: 37.85 hours
Temp
0.200
0.6541
0.6548
0.6544
0.0001
0.0002
0.0003
0.225
0.6524
0.6539
0.6537
0.0002
0.0002
0.0003
0.250
0.6524
0.6508
0.6565
0.0007
0.0003
0.0003
0.275
0.6485
0.6512
0.6529
0.0002
0.0003
0.0003
0.300
0.6518
0.6482
0.6530
0.0001
0.0003
0.0004
0.325
0.6484
0.6508
0.6515
0.0002
0.0002
0.0004
0.350
0.6511
0.6511
0.6500
0.0002
0.0002
0.0003
0.375
0.6512
0.6483
0.6513
0.0002
0.0003
0.0004
0.400
0.6509
0.6457
0.6491
0.0002
0.0003
0.0004
********************
**************
**************
***************
p=0.600 (Wolff, 30,000 samples)
Size
20
40
60
20
40
60
Temp
0.10
0.6448
0.6370
0.6301
0.0006
0.0012
0.0019
0.15
0.6466
0.6390
0.6283
0.0004
0.0012
0.0019
0.20
0.6439
0.6265
0.6286
0.0004
0.0012
0.0021
0.25
0.6475
0.6372
0.6341
0.0004
0.0012
0.0018
0.30
0.6420
0.6400
0.6234
0.0009
0.0012
0.0019
0.35
0.6393
0.6370
0.6181
0.0007
0.0012
0.0019
0.40
0.6384
0.6271
0.6181
0.0004
0.0013
0.0018
0.50
0.6262
0.6108
0.5983
0.0007
0.0014
0.0021
********************
**************
**************
***************
p=0.593 (Sw-W, 16,000 samples)
Mean
20
30
60
20
30
60
Temp
0.100
0.6319
0.6286
0.6264
0.0005
0.0005
0.0004
0.150
0.6372
0.6265
0.6326
0.0003
0.0004
0.0005
0.200
0.6368
0.6336
0.6293
0.0005
0.0004
0.0004
0.250
0.6338
0.6335
0.6243
0.0005
0.0003
0.0004
0.300
0.6389
0.6337
0.6279
0.0005
0.0004
0.0005
0.350
0.6322
0.6273
0.6155
0.0006
0.0005
0.0007
0.400
0.6268
0.6180
0.6057
0.0005
0.0006
0.0007
********************
**************
**************
***************
p=0.590 (Wolff, 60,000 samples, 101 timepoints, average over 50-100)
Size
20
40
60
20
40
60
Temp
0.050
0.6274
0.6257
0.6112
0.0004
0.0013
0.0024
0.075
0.6402
0.6324
0.6075
0.0003
0.0012
0.0023
0.100
0.6346
0.6145
0.6064
0.0004
0.0026
0.0028
0.125
0.6348
0.6224
0.6036
0.0017
0.0014
0.0025
0.150
0.6300
0.6092
0.5872
0.0003
0.0015
0.0025
0.200
0.6237
0.6238
0.6178
0.0005
0.0013
0.0023
0.250
0.6383
0.6135
0.6077
0.0004
0.0024
0.0024
0.300
0.6238
0.6127
0.6060
0.0005
0.0014
0.0027
0.350
0.6329
0.6061
0.5964
0.0004
0.0014
0.0025
0.400
0.6298
0.5968
0.5872
0.0004
0.0015
0.0028
Table 4.4.2
Determination of critical temperatures for a range of bond dilutions
with the 2d squre Ising model using Wolf dynamics
sample sizes from 1,000 to 200,000, and timepoints 0 - 100.
**************
**************
**************
***************
p=0.900 (1000 samples)
Size
20
30
40
20
30
40
Temp
1.80
0.6594
0.6630
0.6643
0.0006
0.0002
0.0002
1.85
0.6546
0.6598
0.6622
0.0011
0.0006
0.0004
1.90
0.6441
0.6500
0.6551
0.0021
0.0013
0.0008
1.95
0.6255
0.6289
0.6340
0.0026
0.0029
0.0019
2.00
0.6015
0.5992
0.5912
0.0036
0.0027
0.0037
2.05
0.5732
0.5486
0.5144
0.0053
0.0046
0.0073
2.10
0.5388
0.4756
0.3839
0.0064
0.0090
0.0118
*****************************
**************
***************
p=0.850 (2000 samples)
Size
20
30
40
20
30
40
Temp
1.60
0.6620
0.6645
0.6654
0.0003
0.0001
0.0001
1.65
0.6594
0.6629
0.6644
0.0004
0.0002
0.0001
1.70
0.6536
0.6590
0.6618
0.0007
0.0004
0.0004
1.75
0.6417
0.6496
0.6540
0.0011
0.0010
0.0007
1.80
0.6228
0.6284
0.6310
0.0021
0.0016
0.0014
1.85
0.5987
0.5948
0.5865
0.0025
0.0023
0.0029
1.90
0.5703
0.5400
0.5047
0.0032
0.0039
0.0059
1.95
0.5295
0.4647
0.3921
0.0046
0.0064
0.0086
2.00
0.4786
0.3750
0.2567
0.0055
0.0096
0.0134
*****************************
**************
***************
p=0.800 (4000 samples)
Size
20
30
40
20
30
40
Temp
1.50
0.6591
0.6622
0.6640
0.0003
0.0002
0.0001
1.55
0.6526
0.6578
0.6611
0.0005
0.0003
0.0002
1.60
0.6401
0.6472
0.6518
0.0007
0.0007
0.0006
1.65
0.6212
0.6232
0.6256
0.0014
0.0013
0.0012
1.70
0.5967
0.5895
0.5777
0.0022
0.0021
0.0026
1.75
0.5681
0.5322
0.4890
0.0026
0.0037
0.0046
1.80
0.5275
0.4554
0.3613
0.0030
0.0045
0.0068
*****************************
**************
***************
p=0.750 (8000 samples)
Size
20
30
40
20
30
40
Temp
1.30
0.6612
0.6638
0.6649
0.0001
0.0001
0.0000
1.35
0.6577
0.6613
0.6635
0.0003
0.0002
0.0001
1.40
0.6508
0.6558
0.6593
0.0005
0.0003
0.0002
1.45
0.6365
0.6440
0.6475
0.0007
0.0005
0.0005
1.50
0.6151
0.6171
0.6200
0.0012
0.0011
0.0010
1.55
0.5915
0.5775
0.5608
0.0014
0.0015
0.0020
1.60
0.5599
0.5259
0.4689
0.0016
0.0022
0.0029
1.65
0.5155
0.4368
0.3380
0.0025
0.0036
0.0056
1.70
0.4605
0.3452
0.2317
0.0033
0.0050
0.0081
**************
*************
**************
***************
p=0.700 (16,000 samples)
Size
20
30
40
20
30
40
Temp
1.10
0.6623
0.6643
0.6652
0.0001
0.0000
0.0000
1.15
0.6603
0.6630
0.6643
0.0001
0.0001
0.0001
1.20
0.6557
0.6595
0.6621
0.0002
0.0002
0.0001
1.25
0.6473
0.6526
0.6563
0.0004
0.0003
0.0002
1.30
0.6309
0.6354
0.6377
0.0006
0.0006
0.0004
1.35
0.6091
0.6072
0.6036
0.0008
0.0007
0.0009
1.40
0.5831
0.5626
0.5364
0.0010
0.0012
0.0015
1.45
0.5476
0.4958
0.4296
0.0015
0.0018
0.0026
1.50
0.4981
0.4105
0.3087
0.0019
0.0030
0.0035
**************
*************
**************
***************
p=0.650 (32,000 samples)
Size
20
30
40
20
30
40
Temp
0.90
0.6624
0.6641
0.6647
0.0001
0.0001
0.0000
0.95
0.6604
0.6630
0.6640
0.0001
0.0001
0.0001
1.00
0.6572
0.6608
0.6624
0.0002
0.0001
0.0001
1.05
0.6511
0.6559
0.6584
0.0002
0.0001
0.0001
1.10
0.6400
0.6442
0.6482
0.0003
0.0003
0.0002
1.15
0.6216
0.6219
0.6222
0.0005
0.0005
0.0005
1.20
0.5986
0.5908
0.5759
0.0006
0.0006
0.0008
1.25
0.5701
0.5371
0.4917
0.0009
0.0011
0.0014
1.30
0.5257
0.4633
0.3795
0.0010
0.0017
0.0025
**************
**************
**************
***************
p=0.600 (64,000 samples)
Size
20
30
40
20
30
40
Temp
0.70
0.6614
0.6621
0.6623
0.0002
0.0002
0.0002
0.75
0.6591
0.6608
0.6614
0.0003
0.0003
0.0002
0.80
0.6562
0.6587
0.6596
0.0003
0.0003
0.0002
0.85
0.6509
0.6536
0.6558
0.0003
0.0003
0.0003
0.90
0.6409
0.6442
0.6469
0.0003
0.0003
0.0003
0.95
0.6248
0.6252
0.6253
0.0004
0.0004
0.0004
1.00
0.6047
0.5962
0.5868
0.0005
0.0007
0.0006
1.05
0.5775
0.5525
0.5225
0.0007
0.0009
0.0010
1.10
0.5412
0.4902
0.4233
0.0009
0.0009
0.0013
**************
**************
**************
***************
p=0.575 (100,000 samples)
Size
20
30
40
20
30
40
Temp
0.72
0.6509
0.6531
0.6541
0.0005
0.0006
0.0005
0.74
0.6493
0.6507
0.6515
0.0006
0.0006
0.0006
0.76
0.6440
0.6479
0.6492
0.0006
0.0006
0.0006
0.78
0.6409
0.6439
0.6453
0.0005
0.0007
0.0006
0.8
0.6368
0.6390
0.6397
0.0006
0.0007
0.0006
0.82
0.6313
0.6332
0.6319
0.0005
0.0007
0.0006
0.84
0.6253
0.6245
0.6229
0.0006
0.0007
0.0007
0.86
0.6173
0.6172
0.6124
0.0007
0.0009
0.0009
0.88
0.6079
0.6060
0.5980
0.0007
0.0009
0.0009
**************
**************
**************
***************
p=0.560 (200,000 samples)
Size
20
30
40
20
30
40
Temp
0.40
0.6603
0.6593
0.6578
0.0006
0.0007
0.0007
0.45
0.6595
0.6585
0.6574
0.0006
0.0007
0.0007
0.50
0.6582
0.6579
0.6566
0.0006
0.0007
0.0007
0.55
0.6569
0.6564
0.6554
0.0006
0.0008
0.0008
0.60
0.6535
0.6545
0.6533
0.0006
0.0008
0.0008
0.65
0.6497
0.6499
0.6501
0.0007
0.0009
0.0008
0.70
0.6432
0.6428
0.6434
0.0008
0.0009
0.0009
0.75
0.6321
0.6304
0.6298
0.0007
0.0010
0.0010
0.80
0.6163
0.6107
0.6044
0.0008
0.0011
0.0012
0.85
0.5956
0.5787
0.5628
0.0010
0.0015
0.0017
0.90
0.5679
0.5372
0.4959
0.0010
0.0017
0.0023
0.95
0.5357
0.4747
0.4072
0.0011
0.0019
0.0027
1.00
0.4945
0.3983
0.3094
0.0011
0.0017
0.0025
**************
**************
**************
***************
p=0.550 (128,000 samples)
Size
20
30
40
20
30
40
Temp
0.30
0.6594
0.6572
0.6555
0.0007
0.0009
0.0009
0.35
0.6590
0.6573
0.6552
0.0007
0.0009
0.0010
0.40
0.6581
0.6566
0.6547
0.0008
0.0010
0.0010
0.45
0.6572
0.6556
0.6538
0.0008
0.0010
0.0010
0.50
0.6547
0.6542
0.6526
0.0008
0.0010
0.0010
0.55
0.6519
0.6516
0.6503
0.0008
0.0011
0.0011
0.60
0.6487
0.6472
0.6465
0.0009
0.0011
0.0012
0.65
0.6411
0.6404
0.6387
0.0009
0.0012
0.0012
0.70
0.6315
0.6271
0.6255
0.0010
0.0013
0.0014
0.75
0.6165
0.6093
0.6033
0.0011
0.0015
0.0017
0.80
0.5950
0.5805
0.5632
0.0012
0.0018
0.0021
0.85
0.5707
0.5418
0.5044
0.0014
0.0023
0.0028
0.90
0.5408
0.4853
0.4163
0.0014
0.0022
0.0031
**************
**************
**************
***************
p=0.525 (200,000 samples)
Size
20
30
40
20
30
40
Temp
0.05
0.6493
0.6448
0.6405
0.0014
0.0020
0.0022
0.10
0.6498
0.6455
0.6406
0.0014
0.0019
0.0022
0.15
0.6488
0.6453
0.6406
0.0013
0.0020
0.0022
0.20
0.6502
0.6454
0.6406
0.0014
0.0019
0.0022
0.25
0.6496
0.6445
0.6403
0.0014
0.0020
0.0022
0.30
0.6488
0.6445
0.6399
0.0014
0.0020
0.0022
0.35
0.6465
0.6432
0.6385
0.0014
0.0020
0.0022
0.40
0.6454
0.6399
0.6350
0.0014
0.0021
0.0023
0.45
0.6416
0.6361
0.6320
0.0015
0.0022
0.0024
0.50
0.6364
0.6307
0.6246
0.0015
0.0023
0.0025
0.55
0.6290
0.6209
0.6144
0.0017
0.0024
0.0027
Table 5.2.1
Absolute magnetization, 2d square Ising, Wolff, timepoints 0 through 50.
M1
M2
Size 100
98% of cr.T
99% of cr.T
crit. T
Temperature
2.224
2.246
2.269
Number of samples
4000
4000
4000
Abs. Magnetization
0.7467
0.6909
0.6015
Std. dev.
0.0008
0.0012
0.0020
Size 200
Temperature
2.224
2.246
2.269
Number of samples
1000
1000
1000
Abs. Magnetization
0.7467
0.6869
0.5555
Std. dev.
0.0008
0.0014
0.0035
Size 400
Temperature
2.224
2.246
2.269
Number of samples
1000
1000
1000
Abs. Magnetization
0.7462
0.6861
0.5128
Std. dev.
0.0004
0.0007
0.0030
Table 5.3.1
Absolute magnetization, Ising triangular, Wolff, timepoints 50 through 100.
M1
M2
Size 100
.98 of cr.T
.99 of cr.T
crit. T
Temperature
3.5682
3.6046
3.6410
Number of samples
4000
4000
4000
Abs. Magnetization
0.7351
0.6804
0.5941
Std. dev.
0.0007
0.0012
0.0019
Size 200
Temperature
3.5682
3.6046
3.6410
Number of samples
1000
1000
1000
Abs. Magnetization
0.7360
0.6766
0.5471
Std. dev.
0.0007
0.0014
0.0034
Size 400
Temperature
3.5682
3.6046
3.6410
Number of samples
1000
1000
1000
Abs. Magnetization
0.7350
0.6755
0.5049
Std. dev.
0.0004
0.0007
0.0030
Table 5.4.1
Absolute magnetization, Ising honeycomb, Wolff, timepoints 50 through 100.
Size 100
.98 of cr.T
.99 of cr.T
Temperature
1.488326
1.503513
Number of samples
8000
8000
M1
M2
Abs. Magnetization
0.76258
0.69991
Std. dev.
0.00062
0.00111
Size 200
Temperature
1.488326
1.503513
Number of samples
4000
4000
Abs. Magnetization
0.76362
0.70209
Std. dev.
0.00040
0.00079
Size 400
Temperature
1.488326
1.503513
Number of samples
2000
2000
Abs. Magnetization
0.76372
0.70242
Std. dev.
0.00028
0.00051
Size 800
Temperature
1.488326
1.503513
Number of samples
1000
1000
Abs. Magnetization
0.76373
0.70234
Std. dev.
0.00020
0.00037
Table 5.5.2
Absolute magnetization, 3-state Potts, square lattice, Wolff dynamics.
Averages over last 50% of 100 timeslices.
M1
M2
Size 100
.98 of cr.T
.99 of cr.T
crit. T
Temperature
0.9751
0.9850
0.9950
Number of samples
16000
16000
16000
Abs. magnetization
0.5250
0.4907
0.4106
Std. dev.
0.0015
0.0014
0.0013
Size 200
Temperature
0.9751
0.9850
0.9950
Number of samples
8000
8000
8000
Abs. magnetization
0.5247
0.4887
0.3843
Std. dev.
0.0021
0.0019
0.0017
Size 400
Temperature
0.9751
0.9850
0.9950
Number of samples
12000
4000
4000
Abs. magnetization
0.5248
0.4882
0.3694
Std. dev.
0.0017
0.0027
0.0022
Table 6.4.1 ----------- Run begun at 1999-08-09 21:48:37 input file: BT.IN output file: BT.OUT model: 4-state Potts dimensionality: 2d lattice type: square dilution type: non-diluted lattice size: 64 temperature: 0.910239 (4-state Potts 2d pure cr. temp.) dynamics: Glauber initial magnetization: 0.02000 number of configurations: 1 number of spin assignments: 400 number of repetitions: 250 number of samples: 100000 number of time slices: 101 step length: 1 MCS Mean Normed Std. Second 2ndmom Auto- Std.dev. magn'n magn'n dev'n moment /first corr'n Autocor. 0 0.02004 1.00000 0.00000 0.00019 0.75000 0.00000 1 0.01692 0.84422 0.00003 0.00025 1.0000 0.29840 0.00002 2 0.01597 0.79671 0.00005 0.00031 1.2552 0.17016 0.00002 3 0.01545 0.77110 0.00005 0.00037 1.4965 0.11418 0.00002 4 0.01514 0.75558 0.00006 0.00043 1.7244 0.08436 0.00002 5 0.01489 0.74303 0.00006 0.00049 1.9374 0.06642 0.00002 6 0.01476 0.73642 0.00007 0.00054 2.1465 0.05467 0.00002 7 0.01467 0.73223 0.00007 0.00059 2.3511 0.04644 0.00002 8 0.01457 0.72703 0.00008 0.00064 2.5398 0.04043 0.00002 9 0.01450 0.72344 0.00008 0.00068 2.7261 0.03582 0.00002 10 0.01448 0.72251 0.00008 0.00073 2.9132 0.03223 0.00002 11 0.01444 0.72047 0.00008 0.00077 3.0905 0.02927 0.00002 12 0.01441 0.71902 0.00009 0.00082 3.2648 0.02688 0.00002 13 0.01439 0.71800 0.00009 0.00086 3.4381 0.02482 0.00002 14 0.01433 0.71525 0.00009 0.00090 3.6019 0.02312 0.00002 15 0.01431 0.71420 0.00010 0.00094 3.7680 0.02160 0.00002 16 0.01428 0.71234 0.00010 0.00098 3.9285 0.02029 0.00002 17 0.01425 0.71090 0.00010 0.00102 4.0881 0.01914 0.00002 18 0.01425 0.71114 0.00010 0.00106 4.2456 0.01813 0.00002 19 0.01417 0.70701 0.00010 0.00110 4.3981 0.01720 0.00002 20 0.01415 0.70592 0.00011 0.00114 4.5549 0.01635 0.00002 21 0.01414 0.70555 0.00011 0.00118 4.7072 0.01562 0.00002 22 0.01413 0.70528 0.00011 0.00121 4.8529 0.01492 0.00002 23 0.01413 0.70530 0.00011 0.00125 4.9980 0.01432 0.00002 24 0.01412 0.70451 0.00011 0.00129 5.1401 0.01376 0.00002 25 0.01410 0.70365 0.00011 0.00132 5.2849 0.01324 0.00002 26 0.01405 0.70125 0.00012 0.00136 5.4290 0.01274 0.00002 27 0.01405 0.70128 0.00012 0.00139 5.5630 0.01229 0.00002 28 0.01404 0.70073 0.00012 0.00143 5.6997 0.01189 0.00002 29 0.01396 0.69657 0.00012 0.00146 5.8340 0.01147 0.00002 30 0.01395 0.69634 0.00012 0.00150 5.9723 0.01112 0.00002 31 0.01394 0.69556 0.00012 0.00153 6.1072 0.01078 0.00002 32 0.01393 0.69526 0.00013 0.00156 6.2452 0.01047 0.00002 33 0.01389 0.69309 0.00013 0.00160 6.3776 0.01018 0.00002 34 0.01387 0.69233 0.00013 0.00163 6.5089 0.00988 0.00002 35 0.01386 0.69164 0.00013 0.00166 6.6376 0.00960 0.00002 36 0.01382 0.68986 0.00013 0.00169 6.7619 0.00935 0.00002 37 0.01381 0.68896 0.00013 0.00173 6.8915 0.00913 0.00002 38 0.01378 0.68771 0.00013 0.00176 7.0179 0.00889 0.00002 39 0.01373 0.68517 0.00014 0.00179 7.1531 0.00865 0.00002 40 0.01378 0.68744 0.00014 0.00182 7.2844 0.00846 0.00002 41 0.01375 0.68615 0.00014 0.00185 7.4027 0.00829 0.00002 42 0.01373 0.68523 0.00014 0.00189 7.5336 0.00810 0.00002 43 0.01370 0.68340 0.00014 0.00192 7.6516 0.00792 0.00002 44 0.01367 0.68205 0.00014 0.00195 7.7791 0.00775 0.00002 45 0.01365 0.68130 0.00014 0.00198 7.8955 0.00761 0.00002 46 0.01362 0.67964 0.00014 0.00201 8.0157 0.00745 0.00002 47 0.01360 0.67860 0.00014 0.00204 8.1322 0.00732 0.00002 48 0.01357 0.67707 0.00015 0.00206 8.2464 0.00717 0.00002 49 0.01361 0.67908 0.00015 0.00210 8.3771 0.00704 0.00002 50 0.01361 0.67918 0.00015 0.00213 8.5048 0.00690 0.00002 51 0.01362 0.67983 0.00015 0.00216 8.6293 0.00677 0.00002 52 0.01358 0.67771 0.00015 0.00219 8.7454 0.00666 0.00002 53 0.01357 0.67732 0.00015 0.00222 8.8650 0.00656 0.00002 54 0.01356 0.67647 0.00015 0.00225 8.9837 0.00643 0.00002 55 0.01354 0.67541 0.00015 0.00228 9.1099 0.00633 0.00002 56 0.01352 0.67490 0.00015 0.00231 9.2320 0.00620 0.00002 57 0.01348 0.67284 0.00016 0.00234 9.3461 0.00610 0.00002 58 0.01344 0.67083 0.00016 0.00237 9.4641 0.00601 0.00002 59 0.01345 0.67130 0.00016 0.00240 9.5788 0.00594 0.00002 60 0.01347 0.67192 0.00016 0.00243 9.6999 0.00583 0.00002 61 0.01346 0.67183 0.00016 0.00246 9.8131 0.00573 0.00002 62 0.01345 0.67094 0.00016 0.00249 9.9370 0.00566 0.00002 63 0.01344 0.67074 0.00016 0.00252 10.0463 0.00555 0.00002 64 0.01346 0.67177 0.00016 0.00254 10.1634 0.00546 0.00002 65 0.01348 0.67259 0.00016 0.00257 10.2778 0.00538 0.00002 66 0.01348 0.67272 0.00016 0.00260 10.3889 0.00530 0.00002 67 0.01344 0.67049 0.00017 0.00263 10.4938 0.00521 0.00002 68 0.01348 0.67248 0.00017 0.00265 10.6025 0.00516 0.00002 69 0.01345 0.67118 0.00017 0.00268 10.7101 0.00510 0.00002 70 0.01344 0.67063 0.00017 0.00271 10.8201 0.00502 0.00002 71 0.01339 0.66828 0.00017 0.00274 10.9247 0.00496 0.00002 72 0.01340 0.66863 0.00017 0.00276 11.0302 0.00491 0.00002 73 0.01337 0.66723 0.00017 0.00279 11.1391 0.00486 0.00002 74 0.01337 0.66740 0.00017 0.00281 11.2402 0.00480 0.00002 75 0.01334 0.66553 0.00017 0.00284 11.3482 0.00471 0.00002 76 0.01333 0.66503 0.00017 0.00287 11.4534 0.00467 0.00002 77 0.01330 0.66388 0.00017 0.00289 11.5593 0.00461 0.00002 78 0.01328 0.66254 0.00017 0.00292 11.6680 0.00457 0.00002 79 0.01328 0.66245 0.00018 0.00295 11.7750 0.00450 0.00002 80 0.01328 0.66292 0.00018 0.00297 11.8787 0.00446 0.00002 81 0.01328 0.66286 0.00018 0.00300 11.9769 0.00443 0.00002 82 0.01328 0.66271 0.00018 0.00303 12.0878 0.00438 0.00002 83 0.01327 0.66231 0.00018 0.00305 12.1867 0.00432 0.00002 84 0.01325 0.66125 0.00018 0.00307 12.2776 0.00427 0.00002 85 0.01326 0.66162 0.00018 0.00310 12.3730 0.00421 0.00002 86 0.01321 0.65942 0.00018 0.00312 12.4622 0.00418 0.00002 87 0.01320 0.65870 0.00018 0.00314 12.5607 0.00413 0.00002 88 0.01325 0.66134 0.00018 0.00317 12.6657 0.00408 0.00002 89 0.01321 0.65914 0.00018 0.00320 12.7763 0.00404 0.00002 90 0.01319 0.65798 0.00018 0.00322 12.8811 0.00400 0.00002 91 0.01314 0.65575 0.00018 0.00325 12.9756 0.00397 0.00002 92 0.01315 0.65636 0.00019 0.00327 13.0783 0.00392 0.00002 93 0.01315 0.65597 0.00019 0.00330 13.1868 0.00386 0.00002 94 0.01317 0.65705 0.00019 0.00333 13.2824 0.00383 0.00002 95 0.01322 0.65957 0.00019 0.00335 13.3893 0.00380 0.00002 96 0.01317 0.65711 0.00019 0.00338 13.4977 0.00376 0.00002 97 0.01318 0.65769 0.00019 0.00340 13.5960 0.00371 0.00002 98 0.01320 0.65850 0.00019 0.00343 13.6963 0.00369 0.00002 99 0.01322 0.65954 0.00019 0.00345 13.7992 0.00365 0.00002 100 0.01319 0.65824 0.00019 0.00348 13.9039 0.00363 0.00002 Run ended at 1999-08-11 06:54:27 Run time = 1 day, 9 hours, 5 minutes, 50 seconds (119150 seconds) ran2() was called 382,344 million times.
Table 6.4.2 ----------- Run began at 2000-06-09 02:27:57 input file: DB.IN (#2 of 3) output file: DB.OUT model: 4-state Potts dimensionality: 2 lattice type: square lattice size: 32 temperature: 0.910239 (2d 4-state Potts cr. temp.) dynamics: Glauber spin selection: checkerboard initial magnetization: 0.00000 number of configurations: 1 number of spin assignments: 500 number of repetitions: 500 number of samples: 250,000 number of time slices: 101 step length: 1 Absolute magnetization requested. Time Mean Std. Second 2ndmom Auto- Std.dev. point magn'n dev'n moment /first corr'n Autocor. 0 0.00000 0.00000 0.00021 0.75000 0.00000 1 0.01724 0.00003 0.00062 1.0000 0.29839 0.00003 2 0.02239 0.00003 0.00092 1.4871 0.17006 0.00003 3 0.02596 0.00004 0.00118 1.9127 0.11401 0.00003 4 0.02885 0.00004 0.00142 2.3013 0.08416 0.00003 5 0.03127 0.00005 0.00164 2.6682 0.06619 0.00003 6 0.03337 0.00005 0.00186 3.0158 0.05444 0.00003 7 0.03528 0.00005 0.00206 3.3440 0.04621 0.00003 8 0.03706 0.00006 0.00226 3.6687 0.04017 0.00003 9 0.03866 0.00006 0.00245 3.9796 0.03556 0.00003 10 0.04018 0.00006 0.00264 4.2848 0.03190 0.00003 11 0.04161 0.00006 0.00282 4.5764 0.02899 0.00003 12 0.04292 0.00006 0.00299 4.8618 0.02661 0.00003 13 0.04416 0.00007 0.00316 5.1398 0.02454 0.00003 14 0.04537 0.00007 0.00334 5.4186 0.02283 0.00003 15 0.04655 0.00007 0.00350 5.6906 0.02130 0.00003 16 0.04762 0.00007 0.00366 5.9528 0.02001 0.00003 17 0.04862 0.00007 0.00382 6.2029 0.01885 0.00003 18 0.04962 0.00007 0.00397 6.4555 0.01782 0.00003 19 0.05068 0.00008 0.00414 6.7171 0.01689 0.00003 20 0.05165 0.00008 0.00429 6.9665 0.01606 0.00003 21 0.05256 0.00008 0.00444 7.2087 0.01530 0.00003 22 0.05351 0.00008 0.00459 7.4542 0.01463 0.00003 23 0.05436 0.00008 0.00473 7.6908 0.01401 0.00003 24 0.05523 0.00008 0.00488 7.9334 0.01344 0.00003 25 0.05605 0.00008 0.00503 8.1694 0.01292 0.00003 26 0.05685 0.00009 0.00517 8.3993 0.01244 0.00003 27 0.05762 0.00009 0.00531 8.6234 0.01200 0.00003 28 0.05842 0.00009 0.00545 8.8540 0.01157 0.00003 29 0.05923 0.00009 0.00559 9.0865 0.01118 0.00003 30 0.05995 0.00009 0.00573 9.3137 0.01083 0.00003 31 0.06066 0.00009 0.00587 9.5362 0.01052 0.00003 32 0.06139 0.00009 0.00601 9.7566 0.01022 0.00003 33 0.06208 0.00009 0.00613 9.9647 0.00991 0.00003 34 0.06276 0.00009 0.00627 10.1856 0.00963 0.00003 35 0.06346 0.00009 0.00640 10.3979 0.00934 0.00003 36 0.06408 0.00010 0.00654 10.6172 0.00912 0.00003 37 0.06474 0.00010 0.00667 10.8335 0.00886 0.00003 38 0.06537 0.00010 0.00680 11.0412 0.00863 0.00003 39 0.06594 0.00010 0.00692 11.2377 0.00839 0.00003 40 0.06655 0.00010 0.00704 11.4410 0.00820 0.00003 41 0.06711 0.00010 0.00716 11.6366 0.00800 0.00003 42 0.06770 0.00010 0.00729 11.8446 0.00781 0.00003 43 0.06828 0.00010 0.00741 12.0428 0.00762 0.00003 44 0.06884 0.00010 0.00754 12.2465 0.00744 0.00003 45 0.06948 0.00010 0.00766 12.4473 0.00731 0.00003 46 0.06997 0.00010 0.00778 12.6338 0.00716 0.00003 47 0.07051 0.00011 0.00790 12.8327 0.00700 0.00003 48 0.07106 0.00011 0.00802 13.0336 0.00691 0.00003 49 0.07162 0.00011 0.00815 13.2299 0.00676 0.00003 50 0.07215 0.00011 0.00826 13.4219 0.00661 0.00003 51 0.07265 0.00011 0.00838 13.6098 0.00649 0.00003 52 0.07317 0.00011 0.00850 13.8042 0.00635 0.00003 53 0.07374 0.00011 0.00862 14.0086 0.00624 0.00003 54 0.07419 0.00011 0.00874 14.1957 0.00614 0.00003 55 0.07465 0.00011 0.00886 14.3872 0.00603 0.00003 56 0.07516 0.00011 0.00898 14.5790 0.00595 0.00003 57 0.07563 0.00011 0.00909 14.7723 0.00584 0.00003 58 0.07609 0.00011 0.00921 14.9569 0.00572 0.00003 59 0.07658 0.00011 0.00932 15.1406 0.00564 0.00003 60 0.07710 0.00012 0.00944 15.3249 0.00557 0.00003 61 0.07754 0.00012 0.00955 15.5053 0.00546 0.00003 62 0.07796 0.00012 0.00966 15.6850 0.00539 0.00003 63 0.07839 0.00012 0.00977 15.8640 0.00531 0.00003 64 0.07888 0.00012 0.00988 16.0494 0.00520 0.00003 65 0.07931 0.00012 0.00999 16.2235 0.00515 0.00003 66 0.07972 0.00012 0.01010 16.4077 0.00507 0.00003 67 0.08017 0.00012 0.01021 16.5856 0.00498 0.00003 68 0.08057 0.00012 0.01032 16.7628 0.00493 0.00003 69 0.08107 0.00012 0.01043 16.9489 0.00484 0.00003 70 0.08147 0.00012 0.01054 17.1171 0.00478 0.00003 71 0.08185 0.00012 0.01065 17.2906 0.00469 0.00003 72 0.08232 0.00012 0.01076 17.4730 0.00463 0.00003 73 0.08269 0.00012 0.01087 17.6500 0.00460 0.00003 74 0.08310 0.00012 0.01098 17.8352 0.00456 0.00003 75 0.08350 0.00013 0.01109 18.0180 0.00449 0.00003 76 0.08393 0.00013 0.01120 18.1956 0.00445 0.00003 77 0.08437 0.00013 0.01132 18.3816 0.00440 0.00003 78 0.08476 0.00013 0.01142 18.5556 0.00434 0.00003 79 0.08515 0.00013 0.01153 18.7283 0.00426 0.00003 80 0.08550 0.00013 0.01164 18.9020 0.00419 0.00003 81 0.08593 0.00013 0.01174 19.0727 0.00412 0.00003 82 0.08626 0.00013 0.01185 19.2438 0.00409 0.00003 83 0.08669 0.00013 0.01195 19.4137 0.00403 0.00003 84 0.08707 0.00013 0.01205 19.5795 0.00400 0.00003 85 0.08743 0.00013 0.01216 19.7503 0.00393 0.00003 86 0.08778 0.00013 0.01226 19.9182 0.00388 0.00003 87 0.08815 0.00013 0.01236 20.0833 0.00385 0.00003 88 0.08855 0.00013 0.01247 20.2594 0.00379 0.00003 89 0.08889 0.00013 0.01257 20.4184 0.00374 0.00003 90 0.08926 0.00013 0.01268 20.5909 0.00371 0.00003 91 0.08969 0.00013 0.01278 20.7622 0.00366 0.00003 92 0.09005 0.00014 0.01289 20.9342 0.00363 0.00003 93 0.09041 0.00014 0.01299 21.1032 0.00362 0.00003 94 0.09079 0.00014 0.01310 21.2752 0.00357 0.00003 95 0.09118 0.00014 0.01321 21.4519 0.00353 0.00003 96 0.09156 0.00014 0.01331 21.6160 0.00351 0.00003 97 0.09189 0.00014 0.01341 21.7795 0.00348 0.00003 98 0.09222 0.00014 0.01350 21.9334 0.00344 0.00003 99 0.09257 0.00014 0.01360 22.0920 0.00337 0.00003 100 0.09292 0.00014 0.01370 22.2549 0.00336 0.00003 Run ended at 2000-06-10 03:30:20 Run time = 1 day, 1 hour, 2 minutes, 23 seconds (90143 seconds) ran2() was called 1,703,326,383 times.
Title page Contents Next: Appendix 6