Low-temperature phase of a stacked triangular Ising antiferromagnet

Abstract

We have investigated a model consisting of planes of Ising spins with antiferromagnetic nearest-neighbor interactions on a triangular lattice connected by nearest-neighbor ferromagnetic bonds in the third direction. It is shown that Landau theory, mean-field theory, and conventional low-temperature expansions are not reliable for this model. We have also studied a class of one-dimensional frustrated Ising models which have low-temperature expansions with irrational coefficients, indicating that the usual method of counting excitations about ground-state configurations cannot be used to construct their low-temperature series. The results from the one-dimensional models are used to obtain bounds on the free energy and information about the magnetization of the three-dimensional model at low temperatures.