Using a classical Monte Carlo simulation on the two-dimensional Heisenberg model with exchange anisotropy, we have obtained reliable results for several properties: spontaneous magnetization, total energy, self-correlation, susceptibility, and correlation functions. An improved algorithm has been used in order to eliminate artifacts in such quantities below the critical temperature. The present results allow us to confirm the validity of spin-wave theory up to temperatures of 0.5${\mathit{T}}_{\mathit{c}}$ and, simultaneously, to predict the phase-transition temperature according to an Ising-like model with a renormalized exchange constant.

• Received 14 August 1992

DOI:https://doi.org/10.1103/PhysRevB.47.5027