Two-dimensional Heisenberg model with weak anisotropy

Harvey S. Leff, Michael Flicker, Kenneth Millard

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, V.V. Khitrintseva

The results of a Monte Carlo study of weakly structural disorder influence onnonequilibrium critical behavior of three-dimensional anisotropic Heisenberg models with spin concentration p = 0.9 are presented with its evolution from high temperature initial state. It is shown that presence of even weakly disorder changes characteristics of nonequilibrium critical behavior of anisotropic model with easy axis anisotropy type in comparison with both pure anisotropic and isotropic Heisenberg models.

R. J. Baxter

Mathew Raymond. Davies, Davies, Mathew Raymond

Real space renormalisation group scaling techniques are used to investigate the static critical behaviour of the pure and dilute, classical, anisotropic Heisenberg model. Transfer matrix methods are employed to obtain asymptotically exact expressions for the correlation lengths and susceptibilities of the one-dimensional system. The resulting scaling relationships are combined with an approximate bond moving scheme to treat pure and dilute models in higher dimensionalities. Detailed discussions are given for the dependence of correlation lengths and susceptibilities on temperature, anisotropy and concentration, and fcr the critical temperature on anisotropy and concentration. Particular emphasis is given to the weakly anisotropic system near percolation threshold and comparisons are made between the results of the present analysis and those of neutron-scattering experiments on dilute quasi-two- and three-dimensional systems.

Ivana Dimitrova, Niklas Jepsen, Jesse Amato-Grill +4 more

Bruce D. Gaulin

The spin configurations of a one-dimensional, weakly anisotropic Heisenberg antiferromagnet were examined by means of an importance sampling Monte Carlo simulation. The spin interactions display weak anisotropies of the same form in each of the orthogonal XY and XZ planes. This allows for two soliton modes, with one in each of the planes. The soliton density within the XZ plane has been determined as a function of the relative strengths of the two anisotropies as well as of temperature. These results are compared with theoretical analysis of similar systems.