Study of Many-State Classical Spin Systems by the Renormalization Group, Duality and Monte Carlo Simulation

Abstract

A class of classical spin systems in two dimensions with symmetry of a cyclic group is studied in three ways : by the real space renormalization group technique, by the duality transformation and by a numerical experiment. The former two methods are shown to be in a close relation to each other. Useful information is obtained on the shape of the critical surface, on the behavior near the criticality and on thermodynamic quantities such as the internal energy and the magnetic susceptibility. Some of these results are compared with expected properties of the planar model, to which the present model reduces if an appropriate limit is taken.