Transfer matrices for the partition function of the Potts model on cyclic and Möbius lattice strips

Physica A: Statistical Mechanics and its Applications

Volumn 347, Issue , 2005, Pages 314-352

  Chang, Shu Chiuan ^a,b   Shrock, Robert ^c  

^a TOKYO UNIVERSITY OF SCIENCE   (Japan)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^c STONY BROOK UNIVERSITY   (United States)

Author keywords

Potts model; Transfer matrices

Indexed keywords

GRAPH THEORY; HAMILTONIANS; LATTICE CONSTANTS; MATHEMATICAL MODELS; POLYNOMIALS; THERMAL EFFECTS;

LATTICE STRIPS; POTTS MODEL; SPIN VARIABLES; TRANSFER MATRICES;

MATRIX ALGEBRA;

EID: 10644262923     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2004.08.023     Document Type: Article

References (43)

1. R.B. Potts, Proc. Cambridge Philos. Soc. 48 (1952) 106.
2. F.Y. Wu, Rev. Mod. Phys. 54 (1982) 235.
3. H. Saleur, Nucl. Phys. B 360 (1991) 219.
4. H. Saleur, Commun. Math. Phys. 132 (1990) 657.
5. S.-C. Chang, R. Shrock, Physica A 296 (2001) 131.
6. R. Shrock, Physica A 283 (2000) 388.
7. S.-C. Chang, R. Shrock, Physica A 296 (2001) 183.
8. S.-C. Chang, R. Shrock, Physica A 301 (2001) 301.
9. N.L. Biggs, Algebraic Graph Theory, 1st ed., Cambridge University Press, Cambridge, 1974 (2nd ed., 1993).
10. R.C. Read, W.T. Tutte, Chromatic polynomials, in: Selected Topics in Graph Theory, vol. 3, Academic Press, New York, 1988, p. 15.
11. S.-C. Chang, R. Shrock, Physica A 296 (2001) 234.
12. S.-C. Chang, R. Shrock, Physica A 286 (2001) 189.
13. S.-C. Chang, R. Shrock, Physica A 301 (2001) 196.
14. S.-C. Chang, R. Shrock, Phys. Rev. E 64 (2001) 066116.
15. S.-C. Chang, R. Shrock, Int. J. Mod. Phys. B 15 (2001) 443.
16. S.-C. Chang, R. Shrock, in: Proceedings of the CRM Workshop on Tutte Polynomials, 2001, Advances in Applied Mathematics, vol. 32, 2004, p. 44.
17. S.-C. Chang, R. Shrock, Physica A 316 (2002) 335.
18. N.L. Biggs, R.M. Damerell, D.A. Sands, J. Combin. Theory B 12 (1972) 123.
19. N.L. Biggs, G.H. Meredith, J. Combin. Theory B 20 (1976) 5.
20. R.J. Baxter, J. Phys. A 19 (1986) 2821.
21. R.J. Baxter, J. Phys. A 20 (1987) 5241.
22. N.L. Biggs, J. Combin. Theory B 82 (2001) 19.
23. N.L. Biggs, Bull. London Math. Soc. 34 (2002) 129.
24. N.L. Biggs, Report LSE-CDAM-2000-04, London School of Economics Centre for Discrete and Applicable Mathematics.
25. J. Salas, A. Sokal, J. Stat. Phys. 104 (2001) 609.
26. S.-C. Chang, J. Salas, R. Shrock, J. Stat. Phys. 107 (2002) 1207.
27. S.-C. Chang, J. Jacobsen, J. Salas, R. Shrock, J. Stat. Phys. 114 (2004) 763.
28. S.-C. Chang, R. Shrock, Physica A, in press, doi:10.1016/j.physa.2004.08. 010.
29. H. Kluepfel, R. Shrock, YITP-99-32; H. Kluepfel, Stony Brook Thesis, July 1999.
30. S.-Y. Kim, R. Creswick, Phys. Rev. E 63 (2001) 066107.
31. R. Shrock, Phys. Lett. A 261 (1999) 57.
32. J.V. Uspensky, Theory of Equations, McGraw-Hill, New York, 1948, p. 264.
33. P.W. Kasteleyn, C.M. Fortuin, J. Phys. Soc. Jpn. Suppl. 26 (1969) 11.
34. C.M. Fortuin, P.W. Kasteleyn, Physica 57 (1972) 536.
35. W.T. Tutte, Can. J. Math. 6 (1954) 80.
36. W.T. Tutte, J. Combin. Theory 2 (1967) 301.
37. W.T. Tutte, Chromials, Lecture Notes Math. 411 (1974) 243
38. W.T. Tutte, Graph Theory, Encyclopedia of Mathematics and Applications, vol. 21, Addison-Wesley, Menlo Park, 1984.
39. B. Bollobás, Modern Graph Theory, Springer, New York, 1998.
40. P. Lancaster, M. Tismenetsky, The Theory of Matrices, Academic Press, New York, 1985.
41. N.L. Biggs, Linear Algebra Appl. 356 (2002) 3.
42. S.-C. Chang, R. Shrock, J. Stat. Phys. 112 (2003) 815.
43. S.-C. Chang, R. Shrock, Physica A 292 (2001) 307.