Eur. Phys. J. B 25, 147-153 (2002)
https://doi.org/10.1140/epjb/e20020017

The two dimensional classical anisotropic Heisenberg ferromagnetic model with nearest- and next-nearest neighbor interactions

Departamento de Física, ICEx, Universidade Federal de Minas Gerais Belo Horizonte, CP 702, CEP 30123-970, MG, Brazil

Corresponding author: ^a meg@aquila.fisica.ufmg.br

Received: 3 April 2001
Revised: 20 September 2001
Published online: 15 January 2002

Abstract

We use the self-consistent harmonic approximation (SCHA) to study the two-dimensional classical Heisenberg anisotropic (easy-plane) ferromagnetic model including nearest- and next-nearest neighbor exchange interactions. For temperatures much lower than the Kosterlitz-Thouless phase transition temperature T_KT, spin waves must be the most relevant excitations in the system and the SCHA must account for its behavior. However, for temperatures near T_KT, we should expect vortex pairs to be quite important. The effect of these vortex excitations on the phase transition temperature is included in our theory as a renormalization of the exchange interactions. Then, combining the SCHA theory to the renormalization effect due to vortex pairs, we calculate the dependence of T_KT as a function of the easy-plane anisotropies and exchange interactions.