MONTE-CARLO MEAN-FIELD THEORY AND FRUSTRATED SYSTEMS IN 2 AND 3 DIMENSIONS

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 than 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 antiferromagnet 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.