order and disorder lines in systems with competing interactions: II. The IRF model
Systems with competing interactions can be often exactly solved on a restricted subspace of the parameter space, called an order or disorder trajectory. A simple method introduced within the transfer matrix formalism allows for the calculation of the free energy and spin-spin correlation functions along the order and disorder lines of the Ising model with all possible interactions around a face of the square lattice (IRF model). The general eight-vertex model is thoroughly examined and shows full analogy with the quantum spin chain results of the previous paper.
Key wordsEight-vertex model interactions around a face order and disorder lines transfer matrix
Unable to display preview. Download preview PDF.
- 1.P. Ruján, preceding paper, this issue.Google Scholar
- 2.I. Peschel and V. J. Emery,Z. Phys. B 43:241 (1981).Google Scholar
- 3.For a review see P. W. Kasteleyn, inFundamental Problems in Statistical Physics, Vol. 3, E. D. G. Cohen, ed., North-Holland, Amsterdam (1975).Google Scholar
- 4.J. Kurman, H. Thomas, and G. Müller,Physica A, to be published.Google Scholar
- 5.R. J. Baxter, inFundamental Problems in Statistical Physics, Vol. 5, E. D. G. Cohen, ed., North-Holland, Amsterdam (1980).Google Scholar
- 6.R. J. Baxter,J. Stat. Phys. 15:485 (1976);17:1 (1977).Google Scholar
- 7.For a review and earlier references see E. H. Lieb and F. Y. Wu, inPhase Transitions and Critical Phenomena, Vol. II, C. Domb and M. S. Green, eds., Academic Press, London (1972).Google Scholar
- 8.C. A. Hurst and H. S. Green,J. Chem. Phys. 33:1059 (1960); C. Fan and F. Y. Wu,Phys. Rev. 179:560 (1969).Google Scholar
- 9.R. J. Baxter,J. Phys. A 13:L61 (1980).Google Scholar
- 10.O. Perron,Math. Ann. 64:248 (1907); S. B. Frobenius,Pressus. Acad. Wiss., 471 (1908).Google Scholar
- 11.P. Ruján,Phys. Rev. B 24:6620 (1981).Google Scholar
- 12.J. Oitmaa,J. Phys. A 14:1159 (1981) and references therein.Google Scholar