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arXiv:1101.2127 · Physical Review E

Evidence for a bicritical point in theXXZHeisenberg antiferromagnet on a simple cubic lattice

Walter Selke

Published Apr 15, 2011• 19 citations
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Abstract

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.

DOI
10.1103/physreve.83.042102

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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.
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.
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 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.
Extensive Monte Carlo simulations are used to locate the bicritical point of the ferromagnetic anisotropic Heisenberg model on a simple cubic lattice in the presence of a crystal field. In order to achieve this goal, we employ a hybrid algorithm comprising Metropolis and Wolff algorithms along with field mixing. Multiple histogram techniques have also been used to obtain the probability distribution function of the conjugate extensive variables of interest. In conjunction with finite-size scaling analysis we computed the fourth-order cumulant of the order parameter along the first-order line and the corresponding bicritical point has been located from the crossings of the cumulants.
We study classical and quantum Heisenberg antiferromagnets with exchange anisotropy of XXZ-type and crystal field single-ion terms of quadratic and quartic form in a field.The magnets display a variety of phases, including the spin-flop (or, in the quantum case, spin-liquid) and biconical (corresponding, in the quantum lattice gas description, to supersolid) phases.Applying ground-state considerations, Monte Carlo and density matrix renormalization group methods, the impact of quantum effects and lattice dimension is analysed.Interesting critical and multicritical behaviour may occur at quantum and thermal phase transitions.
Renormalization-group theory predicts that the XXZ antiferromagnet in a magnetic field along the easy ZZZ axis has asymptotically either a tetracritical phase diagram or a triple point in the field-temperature plane. Neither experiments nor Monte Carlo simulations procure such phase diagrams. Instead, they find a bicritical phase diagram. Here, this discrepancy is resolved: After generalizing a ubiquitous condition identifying the tetracritical point, we employ different renormalization-group recursion relations near the isotropic fixed point, exploiting group-theoretical considerations and using accurate exponents at three dimensions. These show that the results from experiments and simulations can only be understood if their trajectories flow towards the fluctuation-driven first-order transition (and the associated triple point), but reach this limit only for prohibitively large system sizes or correlation lengths. In the crossover region one expects a bicritical phase diagram, as indeed is observed. A similar scenario may explain puzzling discrepancies between simulations and renormalization-group predictions for a variety of other phase diagrams with competing order parameters.