Abstract
We study the effect of spin anisotropies on a frustrated quantum antiferromagnet using the ${J}_{1}\mathrm{\text{\ensuremath{-}}}{J}_{2}^{XXZ}$ model on the square lattice. The $T=0$ and finite-$T$ phase diagrams of this model are obtained utilizing spin-wave theory, exact diagonalization, and quantum Monte Carlo calculations. We find that anisotropic frustration tends to stabilize $XY$- and Ising-like ordered phases, while the disordered spin-liquid phase is restricted to a small region of the phase diagram. The ordered phases are separated by first-order transitions and exhibit a nontrivial reentrance phenomenon.
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