Interface in a one-dimensional Ising spin system

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:61

Article

Bodineau, T

关键词: Gibbs fields;    interfaces;    large deviations;   

DOI  :  10.1016/0304-4149(95)00064-X

来源: Elsevier

【 摘 要 】

In this paper we will be studying the interface in a one-dimensional Ising spin system with a ferromagnetic Kac potential gamma J(gamma/r/). Below the critical temperature, when gamma tends to 0, two distinct thermodynamic phases with different magnetizations appear. We will see that the local magnetization converges to one of these two values. On intervals of length gamma(-k) the local magnetization will stay almost constant, but on longer intervals interfaces take place between different phases. We prove first a large deviation principle and apply Friedlin and Wentzell theory to estimate the position where the first interface appears.

【 授权许可】

Free