Effective meanfield theory based on cumulant expansion in treating the transition of the Potts model on hypercubic lattice
Abstract
An effective meanfield theory based on cumulant expansion is expanded to deal with the firstorder transition of the Potts model on general ddimensional hypercubic lattice in this paper. It is a generalized meanfield method developed from the cumulant expansion of average free energy. As we shall see, it gives the traditional meanfield result at its firstorder approximation and the effective mean field introduced by this method will be amended with the approximation's order increasing. For a full view of this method, we have carried out calculations up to the seventhorder approximation on a square (d=2) lattice since some known exact quantites of this case are terminals that should be approached. The results show this method has the potential to be a useful tool to calculate thermodynamical observables of spin systems.
 Publication:

Physical Review B
 Pub Date:
 April 2001
 DOI:
 10.1103/PhysRevB.63.134419
 Bibcode:
 2001PhRvB..63m4419L
 Keywords:

 05.50.+q;
 75.10.Hk;
 64.60.Cn;
 Lattice theory and statistics;
 Classical spin models;
 Orderdisorder transformations;
 statistical mechanics of model systems