Low-temperature modeling for degenerate and frustrated Heisenberg systems with anisotropy

Thermodynamic equilibration of complex systems like spin glasses or (degenerate) anisotropic spin crystals by numerical methods can be challenging due to the presence of multiple minima on the potential energy surface. This problem becomes pronounced especially at low temperature, where the system remains mainly in few states. We employ the anisotropic Heisenberg model in two dimensions to simulate and analyze the domain formation and the domain structure of multiferroic oxides. In particular, we discuss various techniques to improve the low-temperature equilibration behavior by means of a trigonal antiferromagnet with single-ion anisotropy. Furthermore, we present a localized sampling method for the Metropolis algorithm, which increases the acceptance ratio significantly.