MONTE CARLO STUDY OF THE SPIN-1/2 HEISENBERG MODEL IN 1, 2, AND 3 DIMENSIONS

Abstract

The properties of the spin-1/2 Heisenberg model on 1, 2, and 3-dimensional lattices are calculated using the Decoupled Cell Method of Homma et al., and these results are compared with high temperature and spin-wave expansions, and with other numerical approaches. The DCM has advantages over other Monte Carlo methods currently in wide use in that the transition probability is positive definite, there is no need to introduce an additional imaginary time, or Trotter, dimension, and the acceptance rate for transitions is comparable to that of classical lattice models. We find very good agreement between the DCM and the high temperature expansion in the temperature region where the high temperature expansion is valid, and reasonably good agreement at low temperatures with spin wave theory. The DCM fails for temperatures T < Tc which decreases with the size of the cell.