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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received 30 September 2002 / Received in final form 25 November 2002 Published online 27 January 2003
RID="a"
ID="a"e-mail: pleim@theorie1.physik.uni-erlangen.de
Rights and permissions
About this article
Cite this article
Behringer, H., Pleimling, M. & Hüller, A. Phase transitions in a cluster molecular field approximation. Eur. Phys. J. B 31, 81–93 (2003). https://doi.org/10.1140/epjb/e2003-00012-0
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2003-00012-0