Generation of Cluster Data:
The detail about how to generate a list of cluster data for linked-cluster series expansion is given in the book: "Series Expansion Methods for Strongly Interacting Lattice Models" published by Cambridge University Press.
Here is some examples that low-temperature cluster data that have been generated by our group:
(notation: jtop: graph identifier number; jtop_bare: bare graph identifier number; nv: no. of vertices; nb: no. of bonds; nsym: symmetry number of graph; lc: lattice constant of graph; npair(1,k) and napir(2,k): ends of k'th bond, npair(3,k): bond type of k'th bond;
1. Square lattice:
1.A Cluster data for the ground state properties:
For the calculation of ground state preperties, a list of cluster with 1 bond type has been generated up to 18 sites, there are totally 1500485 graphes.
A list of cluster up to 6 sites are:
1 1 0 1 1.000000000000D+00 2 2 1 2 2.000000000000D+00 1 2 3 3 2 2 6.000000000000D+00 1 2 1 3 4 4 3 6 4.000000000000D+00 1 2 1 3 1 4 5 4 3 2 1.400000000000D+01 1 2 1 3 2 4 6 4 4 8 1.000000000000D+00 1 2 1 3 2 4 3 4 7 5 4 24 1.000000000000D+00 1 2 1 3 1 4 1 5 8 5 4 2 2.000000000000D+01 1 2 1 3 1 4 2 5 9 5 4 2 3.400000000000D+01 1 2 1 3 2 4 3 5 10 5 5 2 8.000000000000D+00 1 2 1 3 1 4 2 5 3 5 11 6 5 6 4.000000000000D+00 1 2 1 3 1 4 1 5 2 6 12 6 5 8 4.000000000000D+00 1 2 1 3 1 4 2 5 2 6 13 6 5 2 3.200000000000D+01 1 2 1 3 1 4 2 5 3 6 14 6 5 2 5.200000000000D+01 1 2 1 3 1 4 2 5 5 6 15 6 5 2 8.200000000000D+01 1 2 1 3 2 4 3 5 4 6 16 6 6 4 4.000000000000D+00 1 2 1 3 1 4 1 5 2 6 3 6 17 6 6 2 1.200000000000D+01 1 2 1 3 1 4 2 5 2 6 3 5 18 6 6 2 1.600000000000D+01 1 2 1 3 1 4 2 5 3 5 4 6 19 6 6 4 8.000000000000D+00 1 2 1 3 1 4 2 5 3 5 5 6 20 6 7 4 2.000000000000D+00 1 2 1 3 1 4 2 5 2 6 3 5 4 6 jtop nv nb nsym lc npair(1:2,1:nb)
The distribution table for no. of bond and vertex, and their total no. of graphes is:
DISTRIBUTION TABLE: (NB DOWN, NV ACROSS)
nv= 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 total
nb= 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
nb= 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
nb= 3 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
nb= 4 0 0 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 9
nb= 5 0 0 0 1 5 0 0 0 0 0 0 0 0 0 0 0 0 15
nb= 6 0 0 0 0 4 8 0 0 0 0 0 0 0 0 0 0 0 27
nb= 7 0 0 0 0 1 8 15 0 0 0 0 0 0 0 0 0 0 51
nb= 8 0 0 0 0 0 3 22 27 0 0 0 0 0 0 0 0 0 103
nb= 9 0 0 0 0 0 0 12 44 53 0 0 0 0 0 0 0 0 212
nb= 10 0 0 0 0 0 0 2 33 108 102 0 0 0 0 0 0 0 457
nb= 11 0 0 0 0 0 0 0 7 95 239 209 0 0 0 0 0 0 1007
nb= 12 0 0 0 0 0 0 0 1 38 247 577 427 0 0 0 0 0 2297
nb= 13 0 0 0 0 0 0 0 0 6 125 665 1322 900 0 0 0 0 5315
nb= 14 0 0 0 0 0 0 0 0 0 32 420 1750 3147 1906 0 0 0 12570
nb= 15 0 0 0 0 0 0 0 0 0 1 150 1260 4631 7357 4117 0 0 30086
nb= 16 0 0 0 0 0 0 0 0 0 0 20 562 3839 12068 17493 8934 0 73002
nb= 17 0 0 0 0 0 0 0 0 0 0 1 119 1972 11220 31424 41331 19633 178702
nb= 18 0 0 0 0 0 0 0 0 0 0 0 10 611 6568 32524 81283 98439 398137
nb= 19 0 0 0 0 0 0 0 0 0 0 0 0 93 2463 21419 92252 209810 724174
nb= 20 0 0 0 0 0 0 0 0 0 0 0 0 4 559 9385 67755 259714 1061591
nb= 21 0 0 0 0 0 0 0 0 0 0 0 0 0 49 2729 33582 209821 1307772
nb= 22 0 0 0 0 0 0 0 0 0 0 0 0 0 2 439 11576 116762 1436551
nb= 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30 2558 45937 1485076
nb= 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 312 12659 1498048
nb= 25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 2226 1500285
nb= 26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 194 1500479
nb= 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 1500485
total= 2 3 6 10 20 39 90 202 502 1248 3290 8740 23937 66129 185690 525284 1500485
1.B Cluster data for the excition dispersion etc:
For the calculation of the excitation dispersion etc, a list of cluster with 4 bond type and 8 symmetries has been generated up to 15 sites, there are totally 4654284 graphes.
A list of cluster up to 6 sites are:
1 1 1 0 1 1
2 2 2 1 2 2 121
3 3 3 2 2 4 121 132
4 3 3 2 2 2 121 133
5 4 4 3 2 4 121 132 143
6 5 4 3 1 8 121 132 241
7 5 4 3 2 4 121 132 244
8 5 4 3 2 2 121 133 241
9 6 4 4 8 1 121 132 242 341
10 7 5 4 8 1 121 132 143 154
11 8 5 4 1 8 121 132 143 251
12 8 5 4 1 8 121 132 143 254
13 8 5 4 2 4 121 132 144 251
14 9 5 4 2 4 121 132 241 352
15 9 5 4 1 8 121 132 241 353
16 9 5 4 2 4 121 132 244 353
17 9 5 4 1 8 121 133 241 352
18 9 5 4 2 2 121 133 241 353
19 9 5 4 2 4 121 133 242 352
20 9 5 4 2 4 121 133 242 354
21 10 5 5 1 8 121 132 143 252 351
22 11 6 5 2 4 121 132 143 154 261
23 12 6 5 2 4 121 132 143 251 264
24 13 6 5 1 8 121 132 143 251 362
25 13 6 5 1 8 121 132 143 254 362
26 13 6 5 2 4 121 133 142 251 363
27 13 6 5 1 8 121 133 142 251 364
28 13 6 5 2 4 121 133 142 254 364
29 14 6 5 1 8 121 132 143 251 561
30 14 6 5 1 8 121 132 143 251 562
31 14 6 5 1 8 121 132 143 251 564
32 14 6 5 1 8 121 132 143 254 561
33 14 6 5 1 8 121 132 143 254 564
34 14 6 5 2 4 121 132 144 251 561
35 14 6 5 1 8 121 132 144 251 562
36 15 6 5 1 8 121 132 241 352 461
37 15 6 5 1 8 121 132 241 352 462
38 15 6 5 1 8 121 132 241 352 464
39 15 6 5 1 8 121 132 241 353 461
40 15 6 5 1 8 121 132 241 353 462
41 15 6 5 1 8 121 132 241 353 464
42 15 6 5 1 8 121 132 244 352 461
43 15 6 5 2 4 121 132 244 352 464
44 15 6 5 2 4 121 132 244 353 461
45 15 6 5 1 8 121 133 241 352 461
46 15 6 5 2 4 121 133 241 352 462
47 15 6 5 2 4 121 133 241 352 464
48 15 6 5 2 2 121 133 241 353 461
49 16 6 6 2 4 121 132 143 154 262 361
50 17 6 6 2 4 121 132 143 252 261 351
51 17 6 6 1 8 121 132 143 252 264 351
52 18 6 6 1 8 121 132 143 252 351 463
53 18 6 6 1 8 121 132 143 252 351 464
54 19 6 6 2 4 121 132 143 252 351 561
55 19 6 6 2 4 121 132 143 252 351 562
56 20 6 7 4 2 121 132 144 252 264 351 461 jtop jtopb nv nb nsym lc npair(1:3,1:nb)
The distribution table for no. of bond and vertex, and their total no. of graphes is:
DISTRIBUTION TABLE: (NB DOWN, NV ACROSS)
nv= 2 3 4 5 6 7 8 9 10 11 12 13 14 15 total
nb= 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2
nb= 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 4
nb= 3 0 0 4 0 0 0 0 0 0 0 0 0 0 0 8
nb= 4 0 0 1 11 0 0 0 0 0 0 0 0 0 0 20
nb= 5 0 0 0 1 27 0 0 0 0 0 0 0 0 0 48
nb= 6 0 0 0 0 7 83 0 0 0 0 0 0 0 0 138
nb= 7 0 0 0 0 1 21 255 0 0 0 0 0 0 0 415
nb= 8 0 0 0 0 0 4 91 847 0 0 0 0 0 0 1357
nb= 9 0 0 0 0 0 0 21 339 2829 0 0 0 0 0 4546
nb= 10 0 0 0 0 0 0 2 89 1360 9734 0 0 0 0 15731
nb= 11 0 0 0 0 0 0 0 9 393 5255 33724 0 0 0 55112
nb= 12 0 0 0 0 0 0 0 1 67 1713 20510 118245 0 0 195648
nb= 13 0 0 0 0 0 0 0 0 6 325 7412 79235 416816 0 699442
nb= 14 0 0 0 0 0 0 0 0 0 45 1655 31505 306353 1478602 2517602
nb= 15 0 0 0 0 0 0 0 0 0 1 275 7913 132354 1179603 3837748
nb= 16 0 0 0 0 0 0 0 0 0 0 23 1508 37264 550695 4427238
nb= 17 0 0 0 0 0 0 0 0 0 0 1 174 7866 169975 4605254
nb= 18 0 0 0 0 0 0 0 0 0 0 0 11 1195 39873 4646333
nb= 19 0 0 0 0 0 0 0 0 0 0 0 0 119 6867 4653319
nb= 20 0 0 0 0 0 0 0 0 0 0 0 0 4 902 4654225
nb= 21 0 0 0 0 0 0 0 0 0 0 0 0 0 57 4654282
nb= 22 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4654284
total= 2 4 9 21 56 164 533 1818 6473 23546 87146 325737 1227708 4654284
2. Triangular Lattice:
3. Honeycomb lattice:
4. Simple cubic lattice
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