Eur. Phys. J. B 54, 249-254 (2006)
https://doi.org/10.1140/epjb/e2006-00435-y

Phase transitions in three dimensional generalized xy models

¹ The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34100 Trieste, Italy and Institute of Solid State Physics, 72 Tzarigradsko Chaussée, 1784 Sofia, Bulgaria
² Unitá di Ricerca CNISM e, Dipartimento di Fisica “A. Volta”, Universitá di Pavia, via A. Bassi 6, 27100 Pavia, Italy

Corresponding author: ^a Silvano.Romano@pv.infn.it

Received: 23 April 2006
Revised: 26 October 2006
Published online: 8 December 2006

Abstract

Generalized xy lattice spin models consist of three-component unit vectors, associated with a D-dimensional lattice (say ), parameterized by usual spherical angles (θ_k,φ_k), and interacting via a ferromagnetic potential restricted to nearest neighbours, of the form here ϵ 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.