论文信息 - Multi-component spin model on a Cayley tree

Multi-component spin model on a Cayley tree

A general spin model on the Cayley tree lattice, which includes both the q component Potts (1952) and the Ashkin-Teller (1943) models, is considered. The free energy in zero field is evaluated in a closed form and found to be analytic in temperature. The model exhibits no long-range order in the sense that the probability of finding two sites far away to be in spin states alpha and beta is constant, independent of alpha and beta . The susceptibility per site, chi R, for a region R in the centre of the lattice, defined to be the summation of the site-site correlations between R and the whole lattice L. For the linear size of R to be any finite fraction of that of L, chi R diverges at the Bethe-Peierls temperature(s) TBP, while for R identical to L, chi R diverges at temperature(s) different from TBP.

Y. K. Wang | F. Y. Wu

[1] H. Falk,et al. Ising spin system on a Cayley tree: Correlation decomposition and phase transition , 1975 .

[2] H. Thomas,et al. Phase transition of the Cayley tree with Ising interaction , 1974 .

[3] J. Zittartz,et al. New Type of Phase Transition , 1974 .

[4] S. Alexander,et al. Three-spin-state generalized Ising model , 1974 .

[5] H. Matsuda,et al. Infinite Susceptibility without Spontaneous Magnetization*) --Exact Properties of the Ising Model on the Cayley Tree-- , 1974 .

[6] T. P. Eggarter. Cayley trees, the Ising problem, and the thermodynamic limit , 1974 .

[7] H. Kunz,et al. Analyticity properties of the Ising model in the antiferromagnetic phase , 1973 .

[8] Michael E. Fisher,et al. Some Basic Definitions in Graph Theory , 1970 .

[9] L. K. Runnels. Phase Transition of a Bethe Lattice Gas of Hard Molecules , 1967 .

[10] H. E. Stanley,et al. Possibility of a Phase Transition for the Two-Dimensional Heisenberg Model , 1966 .

[11] Ryoichi Kikuchi,et al. A Theory of Cooperative Phenomena. III. Detailed Discussions of the Cluster Variation Method , 1953 .

[12] R. B. Potts. Some generalized order-disorder transformations , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[13] J. Ashkin,et al. Two Problems in the Statistical Mechanics of Crystals. I. The Propagation of Order in Crystal Lattices. I. The Statistics of Two-Dimensional Lattices with Four Components. , 1943 .