Effective mean-field theory based on cumulant expansion in treating the transition of the Potts model on hypercubic lattice
Abstract
An effective mean-field theory based on cumulant expansion is expanded to deal with the first-order transition of the Potts model on general d-dimensional hypercubic lattice in this paper. It is a generalized mean-field method developed from the cumulant expansion of average free energy. As we shall see, it gives the traditional mean-field result at its first-order 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 seventh-order 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;
- Order-disorder transformations;
- statistical mechanics of model systems