Phase diagram of the modified XY model

Abstract

A modified two-dimensional XY model, in which the energy of the nearest-neighbour interaction is a function with two minima has been considered. The extrema of Hamiltonian have been classified and transformations to a dual model and Coulomb gas have been performed. It has been shown that a large depth of an additional minimum of the interaction function can lead to the splitting of the phase transition into two. One of them (of the Ising type) is connected with appearance of solitons of an infinite length, and the second one with dissociation of pairs of vortices with half of the circulation quantum. A corresponding phase diagram is constructed. It is proposed that recursion relations of the Migdal-Kadanoff moving bonds approximation can be modified. This new version shows the presence of a line of true fixed points in the XY model, and can be applied for studying the modification of the XY model introduced in this paper. The modified XY model can be applied for describing the behaviour of superfluid 3He thin films.