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Physical review. B, Condensed matter

Effects of solitons in the critical behavior of an anisotropic Heisenberg model in two dimensions

B. V. Costa, Antonio S. T. Pires, M. E. Gouvêa

Published Aug 1, 1994• 6 citations
Publisher

Abstract

Monte Carlo calculations for the classical ferromagnetic Ising-like Heisenberg model suggest that solitons may play an important role in driving the phase transition in that model.Received 10 March 1994DOI:https://doi.org/10.1103/PhysRevB.50.3828©1994 American Physical Society

DOI
10.1103/physrevb.50.3828

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Monte Carlo calculations for the classical ferromagnetic Ising-like Heisenberg model suggest that solitons may play an important role in driving the phase transition in that model.Received 10 March 1994DOI:https://doi.org/10.1103/PhysRevB.50.3828©1994 American Physical Society
The critical and hysteresis behaviors of the ferromagnetic mixed-spin system consisting of two sublattices A and B with two types of spins SA=32 and SB=12 described by anisotropic Classical-Heisenberg Model on a square lattice are examined by using Monte Carlo simulations based on metropolis algorithm. By exploiting the thermal variations of the order-parameters and the magnetic susceptibility, the phase diagrams are calculated on the (Dz/J, kBT/J), (Dx/J, kBT/J) and (Δ, kBT/J) planes and the effects of various interaction parameters in the Hamiltonian are explored. It is found that the model yields only second-order phase transitions. We have also estimated the critical exponents ν, β and γ of the model as functions of Dz and Dx by using the finite-size scaling arguments and found that they depend on the details of the model. Finally, the hysteresis behavior of the model is also investigated and it is revealed that the width of hysteresis loop decreases with temperature while it increases for positive Dz values.
The anisotropic Heisenberg model has been investigated by interpolating anisotropy between the Ising and isotropic Heisenberg limits via general spin high temperature series (HTS) for the zero-field susceptibility of the ferromagnets for the square lattice. This is done by locating the critical temperature ( T c (2) ) and the susceptibility exponent (γ) from the analysis of the series by Pade approximant and ratio methods. The critical temperature is found to be spin dependent. It decreases as anisotropy changes from the Ising limit towards the isotropic limit and remains finite (lower than that of Stanley and Kaplan) for all the spins except for S =1/2 at the isotropic limit. Exponent γ is almost Ising like for the anisotropic system and anomalous jump in it occurs for the isotropic case. In addition, expressions for the magnetization are derived by using spin-wave theory. The limit of complete isotropy has been found not to be a special case for the susceptibility, in contrast to magnetization.
We rigorously prove that in three or more dimensions, the nearest-neighbor, simple-cubic, ferromagnetic, quantum Heisenberg model of spin S(=12,1,…)S(=\frac{1}{2}, 1, \dots{})S(=21​,1,…) has a phase transition at nonzero temperature.