On the Uniqueness of Gibbs Measures for p-Adic Nonhomogeneous λ-Model on the Cayley Tree

被引：0

作者：

Murod Khamraev

Farruh Mukhamedov

Utkir Rozikov

机构：

[1] Institute of Mathematics,Department of Mechanics and Mathematics

[2] National University of Uzbekistan,undefined

[3] Vuzgorodok,undefined

[4] Institute of Mathematics,undefined

来源：

Letters in Mathematical Physics | 2004年 / 70卷

关键词：

Cayley tree; Gibbs measure; Ising model; λ-model; -adic field;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider a nearest-neighbor p-adic ł-model with spin values ±1 on a Cayley tree of order k≥ 1. We prove for the model there is no phase transition and as well as being unique, the p-adic Gibbs measure is bounded if and only if p≥ 3. If p=2, then we find a condition which guarantees the nonexistence of a phase transition. Besides, the results are applied to the p-adic Ising model and we show that for the model there is a unique p-adic Gibbs measure.

引用

页码：17 / 28

页数：11

共 21 条

[1] Aref'eva I. Y.(1991)Wave function of the universe and Modern Phys. Lett. A 6 4341-4358
[2] Dragovich B.(2002)-adic gravity Theoret. Math. Phys. 130 425-431
[3] Frampton P. H.(1987)Existence of a phase transition for the Potts Phys. Lett. B 199 191-194
[4] Volovich I. V.(1974)-adic model on the set Z Progr. Theoret. Phys. 51 82-98
[5] Ganikhodjaev N. N.(1991)Adelic string amplitudes J. Math. Phys. 32 932-936
[6] Mukhamedov F. M.(1996)Bethe lattice and Bethe approximation Indag. Math. N.S. 7 311-330
[7] Rozikov U. A.(2002)Yu.: Indag.Math.N.S. 13 177-183
[8] Freund P. G. O.(2003)-adic quantum mechanics with Markov Process. Related Fields 9 131-162
[9] Witten E.(1988)-adic valued functions Phys.Lett. B 203 52-56
[10] Katsura S.(1998)-adic valued probability measures Siberian Math. J. 39 427-435

← 1 2 3 →