Phase diagrams and multicritical behavior of a three-dimensional anisotropic Heisenberg antiferromagnet

A classical $d=3\mathrm{}$ anisotropic Heisenberg antiferromagnet is studied in the presence of magnetic fields which are either uniform ($H_{\parallel }$) or staggered ($H_{\parallel }^{+}$) along the easy axis or uniform ($H_{\perp }$) perpendicular to it. Ground-state properties ($T=0\mathrm{}$) are determined exactly while the behavior at nonzero temperatures is obtained from first-order spin-wave theory. Extensive data are obtained from Monte Carlo simulations on $L\times L\times L$ simple cubic lattices with periodic boundary conditions and nearest-neighbor coupling with $\frac{J_{\perp }}{J_{\parallel }}=0.8\mathrm{}$. The phase diagram in $H_{\parallel }-T$ space agrees well with the predictions of renormalization-group theory. The behavior very near zero temperature agrees with the spin-wave predictions, but deviations are found at surprisingly low temperatures. In $H_{\parallel }-H_{\parallel }^{+}-T$ space the spin-flop phase spreads out into two "horns" (for $H_{\parallel }^{+}>0\mathrm{}$ and $H_{\parallel }^{+}<0\mathrm{}$) instead of the "bubble" suggested earlier. The substantial hysteresis which we observe at the spin-flop boundary is attributed to relaxation effects. The ways in which first-order phase transitions may be found using the Monte Carlo method are discussed.