Interaction Model in Statistical Mechanics

Journal of Mathematics and Statistics

Kachapova, Farida¹ 

关键词: Infinite Particle System;    Gibbs Measure;    Radius of Interaction;    Thermodynamic Limit;    Ising Model;    Potts Model;   

DOI  :  10.3844/jmssp.2017.339.346

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

Statistical mechanics considers several models such as Ising model, Potts model, Heisenberg model etc. A rigorous mathematical approach based on the axiomatic foundation of probability would benefit the study and applications of these models. In this paper we use this approach to generalize some of these models into one construction named an interaction model. We introduce a mathematically rigorous definition of the model on an integer lattice that describes a physical system with many particles interacting with an external force and with one another; a random field Xt (t∈Zv)  models some property of the system such as electric charge, density etc. We introduce a finite model first and then define the thermodynamic limit of the finite models with Gibbs probability measure. The set of values of Xt can be unbounded for more generality. We study properties of the interaction model and show that Ising and Potts models are particular cases of the interaction model.

【 授权许可】

CC BY