Phase transitions in three dimensional generalized xy models

Generalized xy lattice spin models consist of three-component unit vectors, associated with a D-dimensional lattice (say <InlineEquation ID="Equ1"> <EquationSource Format="TEX">${\mathbb{Z}}^D$</EquationSource> </InlineEquation>), parameterized by usual spherical angles (θ<Subscript>k</Subscript>,φ<Subscript>k</Subscript>), and interacting via a ferromagnetic potential restricted to nearest neighbours, of the form <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$W_{jk}=-\epsilon(\sin \theta_j \sin \theta_k)^p \cos(\phi_j-\phi_k),~p \in {\mathbb{N}},~p \ge 1;$</EquationSource> </InlineEquation> here epsilon is a positive quantity setting energy and temperature scales. The models were recently introduced, and proven to support an ordering transition taking place at finite temperature when D=3; in turn, this transition had been investigated by different techniques for p=2,3,4, and found to belong to the same universality class as the xy model (i.e. p=1). More recently, it was rigorously proven that for sufficiently large p the transition becomes first order. Here we present a detailed analysis of the transitional properties of this class of models for selected values of p. For p=8 simulation results showed a second order phase transition belonging to the xy class of universality; they suggested tricritical behaviour for p=12, and gave evidence of first-order transitions for both p=16 and p=20. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006