Uniaxially anisotropic antiferromagnets in a field along the easy axis
Uniaxially anisotropic antiferromagnets in a field along the easy axis are studied with the help of ground state considerations and Monte Carlo simulations. For classical models, the XXZ model as well as variants, we analyze the role of non-collinear spin configurations of biconical or bidirectional type interpolating between the well-known antiferromagnetic and spin-flop structures. Possible experimental applications to layered cuprate antiferromagnets are discussed. Finally, results of quantum Monte Carlo simulations for the S=1/2 XXZ model on a square lattice are presented, and compared with previous findings.
Puzzle of bicriticality in the XXZ antiferromagnet
Renormalization-group theory predicts that the XXZ antiferromagnet in a magnetic ﬁeld along the easy Z-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 new renormalization-group recursion relations near the isotropic ﬁxed point, exploiting group-theoretical considerations and using accurate exponents at three dimensions. These show that the experiments and simulations results 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.
Wang-Landau algorithm for continuous models and joint density of states.
We present a modified Wang-Landau algorithm for models with continuous degrees of freedom. We demonstrate this algorithm with the calculation of the joint density of states of ferromagnet Heisenberg models and a model polymer chain. The joint density of states contains more information than the density of states of a single variable-energy, but is also much more time consuming to calculate. We present strategies to significantly speed up this calculation for large systems over a large range of energy and order parameter.