Phase transitions in a cluster molecular field approximation

TL;DR

This paper introduces an improved cluster molecular field approximation that uses variable-sized spin clusters with exact density of states calculations to accurately determine non-classical critical exponents in Ising and Potts models.

Contribution

It presents a systematic method to enhance molecular field approximations by incorporating spin clusters, enabling extraction of critical exponents from small system sizes.

Findings

Accurate critical exponents obtained from small clusters.

Effective finite size scaling theory developed.

Reliable critical quantities for Ising and Potts models.

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.