Monte carlo simulations of the quantum xxz model in two dimensions

The XXZ spin Hamiltonian H = - Σ(I, j) (SxiSxj + SyiSyj + ⋋SziSzj) is simulated for quantum spins. The XY model (⋋ = 0) has a Kosterlitz- Thouless phase transition at TKT = 0.45 + 0.05, slightly above which the specific heat has a finite peak. The vortex density has a non-zero value in the low-temperature limit, probably due to quantum fluctuations. The critical temperature holds up at least to ⋋= -0.8. The Ising transition temperature TIsing is measured for Ising-like antiferromagnets ⋋ < - 1 and is found to drop off to zero in a manner consistent with the reciprocal-logarithmic behavior Tc α - 1/log/-⋋1/as proposed for the classical model. © 1985 IOP Publishing Ltd.