Multicritical behavior at the kosterlitz-thouless critical point

Abstract

A multicritical critical point for the two dimensional planar model is analyzed by studying an exactly soluable limit of a related model—the generalized Villain model. The statistical mechanics of this model is written in terms of vortex and symmetry breaking excitations. In these terms, the problem reduces to a kind of two dimensional problem with interacting electric charges and magnetic monopoles. In this form, the problem is manifestly self-dual. The multicritical behavior is exhibited in a three-dimensional phase space in which the axes are the coupling strength of a “square” symmetry breaking which favors four possible directions for the planar model vectors. The analysis of this multicritical point shows that it is the intersection of at least six critical lines—each with continuously varying critical indices. Two of these lines are described by the exactly soluable gaussian model. The other four are isomorphic to one another, and each one has—as a point on the line—a critical point of the Ashkin-Teller model. We argue that each of these lines might be in an equivalent universality class to the line of critical points which occurs in the Baxter and Ashkin-Teller models. We make a suggestion about which point on these critical lines might be in the same universality class as our multicritical point. Correlation functions at the intersection point are calculated and used to develop an expansion of critical indices about this point. This expansion gives a potential method for calculating the critical behavior along the critical lines of the model.