A model with simultaneous first and second order phase transitions

TL;DR

This paper presents a two-dimensional nonlinear XY model exhibiting both a second order phase transition driven by spin waves and a first order transition between two bond-ordered phases, with coexistence of phases at the transition.

Contribution

It introduces a novel XY model with simultaneous first and second order phase transitions and proves phase coexistence at the transition temperature.

Findings

Second order phase transition driven by spin waves.

First order transition between ferromagnetic and antiferromagnetic bond-ordered phases.

Coexistence of bond-ordered phases with a disordered phase at transition.

Abstract

We introduce a two dimensional nonlinear XY model with a second order phase transition driven by spin waves, together with a first order phase transition in the bond variables between two bond ordered phases, one with local ferromagnetic order and another with local antiferromagnetic order. We also prove that at the transition temperature the bond-ordered phases coexist with a disordered phase as predicted by Domany, Schick and Swendsen. This last result generalizes the result of Shlosman and van Enter (cond-mat/0205455). We argue that these phenomena are quite general and should occur for a large class of potentials.