Multicritical behavior and global phase diagrams of tetragonalXY-like antiferromagnets

Abstract

The global $T\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$phase diagram of a model Hamiltonian associated with $\mathrm{XY}$-like antiferromagnetic transitions in tetragonal crystals is studied. It is found that for sufficiently large fourth-order anisotropy ($\frac{K}{J\ensuremath{\gtrsim}0.0814}$), the model exhibits tricritical points at a finite nonzero magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$, in addition to the tetracritical point ($T={T}_{N}, \stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}=0$) predicted previously on the basis of a Landau-Ginzburg-Wilson analysis. The wing critical lines associated with one of the tricritical points are physically accessible in the $T\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ space. In a closely related model appropriate for uniaxial antiferromagnets, we find tricritical and fourth-order critical points at low temperatures.