Table of Contents
Physics Research International
Volume 2011 (2011), Article ID 437093, 5 pages
http://dx.doi.org/10.1155/2011/437093
Research Article

Microcanonical Entropy of the Infinite-State Potts Model

Solid State Physics, Lund University, P.O. Box 118, 221 00 Lund, Sweden

Received 24 March 2011; Revised 2 September 2011; Accepted 7 September 2011

Academic Editor: Ashok Chatterjee

Copyright © 2011 Jonas Johansson and Mats-Erik Pistol. 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

In this investigation we show that the entropy of the two-dimensional infinite-state Potts model is linear in configurational energy in the thermodynamic limit. This is a direct consequence of the local convexity of the microcanonical entropy, associated with a finite system undergoing a first-order transition. For a sufficiently large number of states 𝑞 , this convexity spans the entire energy range of the model. In the thermodynamic limit, the convexity becomes insignificant, and the microcanonical entropy (the logarithm of the density of states) tends to a straight line. In order to demonstrate the behaviour of the convexity, we use the Wang-Landau Monte-Carlo technique to numerically calculate the density of states for a few finite but high values of 𝑞 . Finally, we calculate the free energy and discuss the generality of our results.