Abstract and Applied Analysis
Volume 2011 (2011), Article ID 858725, 21 pages
http://dx.doi.org/10.1155/2011/858725
Research Article

Analysis of Two-Layered Random Interfaces for Two Dimensional Widom-Rowlinson's Model

Jun Wang, Jiguang Shao, and Bingtuan Wang

Department of Mathematics, Key Laboratory of Communication and Information System, Beijing Jiaotong University, Beijing 100044, China

Received 21 May 2011; Revised 31 August 2011; Accepted 12 September 2011

Academic Editor: Dumitru Baleanu

Copyright © 2011 Jun Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The statistical behaviors of two-layered random-phase interfaces in two-dimensional Widom-Rowlinson's model are investigated. The phase interfaces separate two coexisting phases of the lattice Widom-Rowlinson model; when the chemical potential μ of the model is large enough, the convergence of the probability distributions which describe the fluctuations of the phase interfaces is studied. In this paper, the backbones of interfaces are introduced in the model, and the corresponding polymer chains and cluster expansions are developed and analyzed for the polymer weights. And the existence of the free energy for two-layered random-phase interfaces of the two-dimensional Widom-Rowlinson model is given.