Phase Transitions in Ferromagnetic Ising Models with Spatially Dependent Magnetic Fields

被引：10

作者：

Bissacot, Rodrigo ^{[1
]}

Cassandro, Marzio ^{[2
]}

Cioletti, Leandro ^{[3
]}

Presutti, Errico ^{[2
]}

机构：

[1] Univ Sao Paulo, Dept Appl Math, Inst Math & Stat IME USP, Sao Paulo, Brazil

[2] GSSI, I-00167 Laquila, Italy

[3] Univ Brasilia, Dept Math, BR-70910900 Brasilia, DF, Brazil

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2015年 / 337卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Phase Transition; Partition Function; Ising Model; Gibbs Measure; Isoperimetric Inequality;

D O I：

10.1007/s00220-014-2268-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper we study the nearest neighbor Ising model with ferromagnetic interactions in the presence of a space dependent magnetic field that vanishes as vertical bar x vertical bar(-alpha), alpha > 0, as vertical bar x vertical bar -> infinity. We prove that in dimensions d >= 2 for all beta large enough, if alpha > 1 there is a phase transition, while if alpha < 1 there is a unique DLR state.

引用

页码：41 / 53

页数：13

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