Longitudinal spin fluctuations in complex ordered states with a Landau-Ising model

Classical local-moment models, like the Heisenberg and Ising models, are often used in combination with ab initio calculations to predict the magnetic properties of real materials. These can often perform poorly for metals, where fluctuations in the magnitude of the moment are important. Modelling longitudinal spin fluctuations phenomenologically: by allowing spin magnitudes to vary constrained by a Landau-like on-site potential, has been applied frequently by other authors and tends to improve agreement with experiment.
We study a simple model of scalar spins with such an on-site potential, where the energy scale of the fluctuations is characterised by a single parameter: the rigidity of the magnetic moment. We explore the implications of these fluctuations on collinear magnetic states with Monte Carlo simulations. This is particularly challenging for the Metropolis algorithm, so we discuss the numerical implementation of an alternative method, the Heat-bath algorithm. We study a variety of ordered states on a stacked triangular lattice, including frustrated and modulated phases. The influence of fluctuations on the nature of these phases is discussed in depth, and we uncover interesting behaviour which is sensitively dependent on the configuration of interaction parameters.