J. Phys. Soc. Jpn. 75 (2006) 114003 (5 pages)  |Previous Article| |Next Article|  |Table of Contents|
|Full Text PDF: OPEN SELECT (127K)|

Internal Energy of the Potts Model on the Triangular Lattice with Two- and Three-Body Interactions

Masayuki Ohzeki and Hidetoshi Nishimori

(Received May 25, 2006; Accepted September 14, 2006; Published November 10, 2006)

We calculate the internal energy of the Potts model on the triangular lattice with two- and three-body interactions at the transition point satisfying certain conditions for coupling constants. The method is a duality transformation. Therefore we have to make assumptions on uniqueness of the transition point and that the transition is of second order. These assumptions have been verified to hold by numerical simulations for q=2, 3, and 4, and our results for the internal energy are expected to be exact in these cases. ©2006 The Physical Society of Japan

KEYWORDS: Potts model, exact energy, triangular lattice, duality transformation, transition point
URL: http://jpsj.ipap.jp/link?JPSJ/75/114003/
DOI: 10.1143/JPSJ.75.114003

References

1. H. A. Kramers and G. H. Wannier: Phys. Rev. 60 (1941) 252[APS].
2. R. B. Potts: Proc. Cambridge Philos. Soc. 48 (1952) 106.
3. T. Kihara, Y. Midzuno and T. Shizume: J. Phys. Soc. Jpn. 9 (1954) 681[IPAP].
4. D. Kim and R. I. Joseph: J. Phys. C 7 (1974) L167[IoP STACKS].
5. I. Syozi: in Phase Transition and Critical Phenomena, ed. C. Domb and M. S. Green (Academic Press, 1972) Vol. 1.
6. R. J. Baxter, H. N. V. Temperly and S. E. Ashley: Proc. R. Soc. London, Ser. A 358 (1978) 535.
7. F. Y. Wu and K. Y. Lin: J. Phys. A 13 (1980) 629[IoP STACKS].
8. F. Y. Wu: Rev. Mod. Phys. 54 (1982) 235[APS].
9. M. Schick and R. B. Griffiths: J. Phys. A 10 (1977) 2123[IoP STACKS].
10. F. Y. Wu and R. K. P. Zia: J. Phys. A 14 (1981) 721[IoP STACKS].