Ground state entropy of Potts antiferromagnets and the approach to the two-dimensional thermodynamic limit

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 58, Issue 4, 1998, Pages 4332-4339

  Shrock, Robert ^a   Tsai, Shan Ho ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000240640     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.4332     Document Type: Article

References (46)

1. L. Pauling, The Nature of the Chemical Bond (Cornell University Press, Ithaca, 1960), p. 466.
2. E. H. Lieb and F. Y. Wu, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic Press, New York, 1972), Vol. 1, p. 331.
3. M. Aizenman and E. H. Lieb, J. Stat. Phys. 24, 279 (1981).JSTPBS
4. Y. Chow and F. Y. Wu, Phys. Rev. B 36, 285 (1987)
5. Y. Chow, Discrete Math. 66, 51-58 (1987).DSMHA4
6. R. B. Potts, Proc. Cambridge Philos. Soc. 48, 106 (1952).PCPSA4
7. F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982)
8. Rev. Mod. Phys.F. Y. Wu 55, 315(E) (1983).
9. R. C. Read, J. Combin. Theory 4, 52 (1968)
10. R. C. Read and W. T. Tutte, in Selected Topics in Graph Theory, 3, edited by L. W. Beineke and R. J. Wilson (Academic Press, New York, 1988).
11. E. H. Lieb, Phys. Rev. 162, 162 (1967).PHRVAO
12. R. J. Baxter, J. Phys. A 20, 5241 (1987).JPHAC5
13. J. F. Nagle, J. Comb. Theory, Ser. B 10, 42 (1971); JCBTB8
14. J. Comb. Theory, Ser. BG. A. Baker, Jr., 10, 217 (1971).
15. D. Kim and I. G. Enting, J. Comb. Theory, Ser. B 26, 327 (1979).JCBTB8
16. R. Shrock and S.-H. Tsai, Phys. Rev. E 55, 6791 (1997).PLEEE8
17. R. Shrock and S.-H. Tsai, Phys. Rev. E 56, 2733 (1997).PLEEE8
18. R. Shrock and S.-H. Tsai, Phys. Rev. E 56, 4111 (1997); PLEEE8
19. Phys. Rev. ES.-H. Tsai, 57, 2686 (1998).
20. N. L. Biggs, Bull. London Math. Soc. 9, 54 (1977).ZZZZZZ
21. X. Chen and C. Y. Pan, Int. J. Mod. Phys. B 1, 111 (1987)
22. Int. J. Mod. Phys. BC. Y. Pan and X. Chen, 2, 1503 (1988).
23. J.-S. Wang, R. H. Swendsen, and R. Kotecký, Phys. Rev. B 42, 2465 (1990).PRBMDO
24. R. Shrock and S.-H. Tsai, J. Phys. A 30, 495 (1997).JPHAC5
25. N. L. Biggs, R. M. Damerell, and D. A. Sands, J. Comb. Theory, Ser. B 12, 123 (1972).JCBTB8
26. S. Beraha, J. Kahane, and N. Weiss, J. Comb. Theory, Ser. B 28, 52 (1980).JCBTB8
27. R. C. Read and G. F. Royle, in Graph Theory, Combinatorics, and Applications (Wiley, New York, 1991), Vol. 2, p. 1009.
28. R. Shrock and S.-H. Tsai, Phys. Rev. E 55, 5165 (1997).PLEEE8
29. R. Shrock and S.-H. Tsai, Phys. Rev. E 56, 1342 (1997).PLEEE8
30. R. Shrock and S.-H. Tsai, Phys. Rev. E 56, 3935 (1997), and PLEEE8
31. (unpublished).
32. M. Roček, R. Shrock, and S.-H. Tsai, Physica A 252, 505 (1998)
33. Physica A (to be published).
34. R. Shrock and S.-H. Tsai, Physica A (to be published).
35. A. E. Ferdinand and M. E. Fisher, Phys. Rev. 185, 832 (1969).PHRVAO
36. A. A. Belavin, A. M. Polyakov, and A. B. Migdal, Nucl. Phys. B 241, 333 (1984)
37. D. Friedan, Z. Qiu, and S. Shenker, Phys. Rev. Lett. 52, 1575 (1984)
38. C. Itzykson, H. Saleur, and J.-B. Zuber, Conformal Invariance and Applications to Statistical Mechanics (World Scientific, Singapore, 1988)
39. J. Cardy, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1987), vol. 11, p. 55.
40. J. Kondev and C. Henley, Nucl. Phys. B 464, 540 (1996).NUPBBO
41. H. Park and M. den Nijs, Phys. Rev. B 38, 565 (1988)
42. H. ParkM. den NijsJ. Phys. A 22, 3663 (1989)
43. H. Park and M. Widom, Phys. Rev. Lett. 63, 1193 (1989).PRLTAO
44. J. L. Cardy, J. Phys. A 17, L385, L961 (1984); JPHAC5
45. H. W. J. Blöte, J. L. Cardy, and M. P. Nightingale, Phys. Rev. Lett. 56, 742 (1986)
46. I. Affleck, Phys. Rev. Lett. 56, 746 (1986).