Monte Carlo mean-field theory and frustrated systems in two and three dimensions

Abstract

A new method, combining mean-field and Monte Carlo approaches, is applied to frustrated Ising systems in d=2 and 3, in zero and nonzero uniform fields. The method brings to mean-field theory the hard-spin condition and uses much less sampling then the Monte Carlo simulation. The phase diagram of the d=2 triangular antiferromagnet is easily obtained with remarkable global quantitative accuracy. The phase diagram of the d=3 stacked triangular antiferromgnet shows three ordered phases, in a new multicritical topology of lines of XY, Ising, and three-state Potts transitions, accessible to experiments with layered magnets.