Bicritical universality of the anisotropic Heisenberg model in a crystal field

Abstract

The bicritical properties of the three-dimensional classical anisotropic Heisenberg model in a crystal field are investigated through extensive Monte Carlo simulations on a simple cubic lattice, using Metropolis and Wolff algorithms. Field-mixing and multidimensional histogram techniques were employed in order to compute the probability distribution function of the extensive conjugate variables of interest and, using finite-size scaling analysis, the first-order transition line of the model was precisely located. The fourth-order cumulant of the order parameter was then calculated along this line and the bicritical point located with good precision from the cumulant crossings. The bicritical properties of this point were further investigated through the measurement of the universal probability distribution function of the order parameter. The results lead us to conclude that the studied bicritical point belongs in fact to the three-dimensional Heisenberg universality class.

Anisotropic XY antiferromagnets in a field

“…Much of the theoretical work is based on analyzing the prototypical classical Heisenberg model with uniaxial anisotropy, the XXZ model, in a field, plus, possibly, further anisotropy terms, such as single-ion anisotropies. Especially, mean-field approximation [2,4], Monte Carlo simulations [16,17,18,19,20,21,22,23], and renormalization group calculations [3,5,24,25,26] have been applied.…”

“…Especially, mean-field approximation [2,4], Monte Carlo simulations [16,17,18,19,20,21,22,23], and renormalization group calculations [3,5,24,25,26] have been applied.…”