Kosterlitz-Thouless transitions in simple spin-models with strongly varying vortex densities

Abstract

A generalized XY-model, consisting of a family of nearest neighbour potentials of varying shape, for classical planar spins on a two-dimensional square lattice is analysed by a combination of Migdal-Kadanoff real-space renormalization and Monte Carlo simulations on a sequence of finite lattices of up to 256×256 spins. For all potential shapes, Kosterlitz-Thouless transitions are found with the same universal features as in the pure XY-model, whereas the density of vortices in the transition region depends strongly upon the shape of the potential.