The puzzle of bicriticality in the XXZ antiferromagnet

Abstract

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.

The details of the new remormalization group analysis are explained in detail, and quantitative estimates for bicriticality are added

References in corpus (9)

• Bootstrapping Heisenberg Magnets and their Cubic Instability
• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• Field theory of bi- and tetracritical points: Statics
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• Different critical behaviors in cubic to trigonal and tetragonal perovskites
• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• Antiferromagnetic spin Seebeck effect across the spin-flop transition: A stochastic Ginzburg-Landau simulation
• Unconventional pressure-driven metamagnetic transitions in topological van der Waals magnets
• Finite size scaling for a first order transition where a continuous symmetry is broken: The spin-flop transition in the 3D XXZ Heisenberg antiferromagnet

Cited by in corpus (3)

• ${\varphi }^4$ lattice model with cubic symmetry in three dimensions: RG-flow and first order phase transitions
• Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary
• Finite size effects in the phase transition patterns of coupled scalar field systems