On the relation between the Coulomb gas and the lattice XY model

Abstract

By using Monte Carlo methods, the authors study the Coulomb gas in two dimensions. They focus their measurements in the regime in which an area law is expected. Their results confirm such a behaviour. The authors compare these results with those obtained for the vorticity in the lattice XY model: the comparison shows a sharp contrast in the behaviour of these two models. They conclude that, contrary to the common belief, the topological vortices of the XY model are not correctly described by a dilute Coulomb gas. Their results were obtained using an 8-node concurrent processor built at Caltech.