M. E. Gouvea

LOW-TEMPERATURE STATIC AND DYNAMIC BEHAVIOR OF THE TWO-DIMENSIONAL EASY-AXIS HEISENBERG MODEL

We apply the self-consistent harmonic approximation (SCHA) to study static and dynamic properties of the two-dimensional classical Heisenberg model with easy-axis anisotropy. The static properties obtained are magnetization and spin wave energy as functions of temperature, and the critical temperature as a function of the easy-axis anisotropy. We also calculate the dynamic correlation functions using the SCHA renormalized spin wave energy. Our analytical results, for both static properties and dynamic correlation functions, are compared to numerical simulation data combining cluster\char21{}Monte Carlo algorithms and spin dynamics. The comparison allows us to conclude that far below the transition temperature, where the SCHA is valid, spin waves are responsible for all relevant features observed in the numerical simulation data; topological excitations do not seem to contribute appreciably. For temperatures closer to the transition temperature, there are differences between the dynamic correlation functions from SCHA theory and spin dynamics; these may be due to the presence of domain walls and solitons.

Topological and dynamical excitations in a classical 2D easy-axis Heisenberg model

Abstract:The properties of dynamical solitons (magnon droplets) in the classical, two-dimensional anisotropic Heisenberg model with easy-axis exchange anisotropy are studied. The solution of the Landau-Lifshitz equation in the continuum limit for the soliton with topological charge q = 1 is obtained numerically using a shooting method. We analized a wide range of the anisotropy parameter and our results are in good agreement with results obtained from spin dynamics simulations. The dependence of an internal precession frequency of the soliton on both the anisotropy parameter and the radius of the soliton is also investigated. Finally, the limits of applicability of the continuum approach are discussed.

Exchange renormalization in one dimensional classical antiferromagnets in the continuum limit

Abstract In this paper we study the effects of the anharmonic terms, usually neglected when a continuum limit is taken, to the exchange part of the continuum Hamiltonian for the classical easy-plane one dimensional antiferromagnet. This correction leads to a dependence with temperature of the soliton energy.