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
Generalized xy lattice spin models consist of
three-component unit vectors, associated with a D-dimensional
lattice (say 
), parameterized by usual spherical
angles (θk,φk), 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.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 75.10.-b – General theory and models of magnetic ordering / 75.10.Hk – Classical spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006
