Three-dimensional generalized models: A Monte Carlo study

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

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

Received: 19 May 2005
Accepted: 27 July 2005

Abstract

The lattice spin models considered in the present paper consist of three-component unit vectors, associated with a D-dimensional lattice (say ), parameterized by usual spherical angles , 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 rigorous comparison inequalities holding for them were investigated, and used to prove the existence of an ordering transition when (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 and ; our results are consistent with the same universality class as the xy model.