Critical properties of the two-dimensional anisotropic Heisenberg model
- 1 February 1976
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 13 (3), 1140-1155
- https://doi.org/10.1103/physrevb.13.1140
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.
Keywords
This publication has 56 references indexed in Scilit:
- The Two-Dimensional Ising ModelPublished by Harvard University Press ,1973
- Crystalline Order in Two DimensionsPhysical Review B, 1968
- Dependence of Critical Properties on Dimensionality of SpinsPhysical Review Letters, 1968
- Spin-ordering in a planar classical Heisenberg modelThe European Physical Journal A, 1967
- Existence of Long-Range Order in One and Two DimensionsPhysical Review B, 1967
- Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg ModelsPhysical Review Letters, 1966
- Possibility of a Phase Transition for the Two-Dimensional Heisenberg ModelPhysical Review Letters, 1966
- Long-wavelength excitations and the Goldstone theorem in many-particle systems with ?broken symmetries?The European Physical Journal A, 1966
- On the Curie points and high temperature susceptibilities of Heisenberg model ferromagneticsMolecular Physics, 1958
- Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder TransitionPhysical Review B, 1944