On Free Energies of the Ising Model on the Cayley Tree

被引：26

作者：

Gandolfo, D. ^{[1
,2
]}

Rakhmatullaev, M. M. ^{[3
]}

Rozikov, U. A. ^{[4
]}

Ruiz, J. ^{[1
,2
]}

机构：

[1] Univ Aix Marseille, Ctr Phys Theor, UMR 6207, F-13288 Marseille, France

[2] Univ Sud Toulon Var, Ctr Phys Theor, UMR 6207, F-13288 Marseille, France

[3] Namangan State Univ, Namangan, Uzbekistan

[4] Inst Math, Tashkent 100125, Uzbekistan

来源：

JOURNAL OF STATISTICAL PHYSICS | 2013年 / 150卷 / 06期

关键词：

Cayley tree; Ising model; Boundary condition; Gibbs measure; Free energy; Entropy; GIBBS MEASURES; STATE;

D O I：

10.1007/s10955-013-0713-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present, for the Ising model on the Cayley tree, some explicit formulae of the free energies (and entropies) according to boundary conditions (b.c.). They include translation-invariant, periodic, Dobrushin-like b.c., as well as those corresponding to (recently discovered) weakly periodic Gibbs states. The weakly periodic measures are defined through a partition of the Cayley tree that induces a 4-edge-coloring on that tree. We compute the density of each color. We use these densities for computations of free energies corresponding to a weakly periodic b.c.

引用

页码：1201 / 1217

页数：17

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