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 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.

Automated summary

This study resolves the discrepancy between the predicted phase diagram and experimental results for the XXZ antiferromagnet. By generalizing a ubiquitous condition and using renormalization-group recursion relations, the study shows that experiments and simulations can only approach the fluctuation-driven first-order transition and the associated triple point for prohibitively large system sizes or correlation lengths.