Eur. Phys. J. B 31, 81-93 (2003)
https://doi.org/10.1140/epjb/e2003-00012-0

Phase transitions in a cluster molecular field approximation

¹ Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
² Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France

Corresponding author: ^a pleim@theorie1.physik.uni-erlangen.de

Received: 30 September 2002
Revised: 25 November 2002
Published online: 27 January 2003

Abstract

Cluster molecular field approximations represent a substantial progress over the simple Weiss theory where only one spin is considered in the molecular field resulting from all the other spins. In this work we discuss a systematic way of improving the molecular field approximation by inserting spin clusters of variable sizes into a homogeneously magnetised background. The density of states of these spin clusters is then computed exactly. We show that the true non-classical critical exponents can be extracted from spin clusters treated in such a manner. For this purpose a molecular field finite size scaling theory is discussed and effective critical exponents are analysed. Reliable values of critical quantities of various Ising and Potts models are extracted from very small system sizes.