Abstract
While a nonzero spontaneous magnetization cannot exist in a Heisenberg spin system, it is possible that a phase transition associated with a divergent susceptibility occurs at the Stanley-Kaplan temperature . The crossover from this special isotropic case to the anisotropic (Ising) behavior is studied using a Monte Carlo technique. The classical model with Hamiltonian on square lattices with periodic boundary conditions is investigated for and varying from 0.005 to 1. The spontaneous magnetization , energy, specific heat, longitudinal and transverse susceptibilities, and the self-correlation are determined over a wide temperature range. For weak anisotropy decreases nonmonotonically with increasing temperature and deviations from simple spin-wave theory occur at surprisingly low temperatures. Transition temperatures exceed the isotropic value predicted by series expansions although the values would also be consistent with if . The asymptotic critical exponent for the order parameter is for all . The susceptibility data show crossover from near to higher values farther from . It is shown that finite-size rounding may lead to erroneously large estimates for and erroneously small estimates for . These effects may invalidate some conclusions drawn from experiments on planar systems, too. Accepting the series estimate we find that the data are consistent with with . Assuming power-law behavior we show that our data obey crossover scaling with two-dimensional Heisenberg exponents , in the isotropic limit. The data are also consistent with scaling theory based on the assumption of singularities which are stronger than any power law.
- Received 14 July 1975
DOI:https://doi.org/10.1103/PhysRevB.13.1140
©1976 American Physical Society