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Journal of Physics Conference Series

Bicritical or tetracritical: the 3D anisotropic Heisenberg antiferromagnet

Shan-Ho Tsai, Siyan Hu, David Paul Landau

Published Mar 11, 2014• 3 citations
Publisher

Abstract

The classical uniaxially anisotropic Heisenberg antiferromagnet on the simple cubic lattice, in the presence of an external magnetic field, is believed to have a multicritical point; however, there has been controversy whether it is a bicritical or a tetracritical point. We perform Monte Carlo simulations of this model and analyze the components of the staggered magnetization, the susceptibilities and the probability distribution of the magnetization to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.

DOI
10.1088/1742-6596/487/1/012005

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The classical uniaxially anisotropic Heisenberg antiferromagnet on the simple cubic lattice, in the presence of an external magnetic field, is believed to have a multicritical point; however, there has been controversy whether it is a bicritical or a tetracritical point. We perform Monte Carlo simulations of this model and analyze the components of the staggered magnetization, the susceptibilities and the probability distribution of the magnetization to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.
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.
We use Monte Carlo simulations to study the XXZ Heisenberg antiferromagnet in a field in order to clearly determine the nature of the multicritical point. We use a hybrid sampling method with Metropolis and Wolff-cluster algorithms, along with histogram reweighting techniques. Staggered magnetization susceptibilities, Binder cumulants, and finite-size scaling are considered in an effort to detect a possible biconical phase. An analysis of the probability distribution of the magnetization allowed us to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.
The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy (XXZ model) in a field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. We analyze, in particular, various staggered susceptibilities and Binder cumulants and present clear evidence for the triple point of the antiferromagnetic, spin-flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions applying various theoretical approaches.
By considering the appropriate finite-size effect, we explain the connection between Monte Carlo simulations of two-dimensional anisotropic Heisenberg antiferromagnet in a field and the early renormalization group calculation for the bicritical point in 2+ϵ2+ϵ2+ϵ dimensions. We found that the long-length-scale physics of the Monte Carlo simulations is indeed captured by the anisotropic nonlinear $\ensuremath{\sigma}$ model. Our Monte Carlo data and analysis confirm that the bicritical point in two dimensions is Heisenberg-like and occurs at T=0T=0T=0; therefore the uncertainty in the phase diagram of this model is removed.
A complete two-loop renormalization group calculation of the multicritical dynamics at a tetracritical or bicritical point in three-dimensional anisotropic antiferromagnets in an external magnetic field is performed. Although strong scaling for the two order parameters (OPs) perpendicular and parallel to the field is restored as found earlier, in the experimentally accessible region the effective dynamical exponents for the relaxation of the OPs remain different since their equal asymptotic values are not reached.
Recently, the ordering scenario of three-dimensional site frustrated Heisenberg models has been challenged. The existence of a decoupled tetracritical point (DTP) where ferromagnetic (FM) and antiferromagnetic (AF) order occur simultaneously has been modified to include a line of multicritical points where both FM and AF occur simultaneously. In addition, numerous studies claim that, within the mixed phase, critical exponents are altered from Heisenberg values. Here we show that within the narrow region of proposed multicritical points, the transition temperatures away from the tetracritical point are indeed distinct, confirming the occurrence of a DTP. In addition, we show a universal scaling collapse of the magnetization both away from, and within, the mixed phase using Heisenberg exponents, demonstrating that the stable fixed points are within the Heisenberg universality class.