Europhys. Lett.
Volume 72, Number 1, October 2005
Page(s) 62 - 68
Section General
Published online 31 August 2005
Europhys. Lett., 72 (1), pp. 62-68 (2005)
DOI: 10.1209/epl/i2005-10197-8

Three-dimensional generalized $\mth{xy}$ models: A Monte Carlo study

H. Chamati1, S. Romano1, L. A. S. Mól2 and A. R. Pereira2

1  Istituto Nazionale per la Fisica della Materia e Dipartimento di Fisica "A. Volta" Università di Pavia - via A. Bassi 6, I-27100 Pavia, Italy
2  Departamento de Física, Universidade Federal de Viçosa Viçosa, 36570-000, Minas Gerais, Brazil

received 19 May 2005; accepted in final form 27 July 2005
published online 31 August 2005

The lattice spin models considered in the present paper consist of three-component unit vectors, associated with a D-dimensional lattice (say ${\mathbb{Z} }^d$), parameterized by usual spherical angles $(\theta_k,\phi_k)$, and interacting via a ferromagnetic potential restricted to nearest neighbours, of the form $W_{jk}=-\epsilon(\sin \theta_j
\sin \theta_k)^p \cos(\phi_j-\phi_k),~p \in {\mathbb{N} },~p \ge 1;$ here $\epsilon$ is a positive quantity setting energy and temperature scales. The models were recently introduced, and rigorous comparison inequalities holding for them were investigated, and used to prove the existence of an ordering transition when D=3 (ROMANO S. AND ZAGREBNOV V. A., Phys. Lett. A, 301 (2002) 402), investigated by other approximate techniques as well (MÓL L. A. S., PEREIRA A. R. AND MOURA-MELO W. A., Phys. Lett. A, 319 (2003) 114). We report here an extensive Monte Carlo study of the critical behaviour for D=3 and $p\le 4$; our results are consistent with the same universality class as the xy model.

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 2005