Low-temperature expansion of a spatially frustrated isotropic lattice model

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Abstract
A low-temperature expansion of an isotropic, spatially frustrated lattice model with nearest-neighbor, second-, and third-nearest-neighbor interactions is presented. The zero-temperature states of this model are known exactly. For some regions of parameter space there is an infinity of zero-temperature states, although the ground-state entropy per spin is zero at zero temperature. In general one expects fluctuations at finite temperature to break the degeneracy on the zero-temperature-state manifold. When the zero-temperature states are regular or periodic, it is possible to characterize them and to apply the low-temperature expansion to break this degeneracy in a rigorous way. In the present paper we carry out such a calculation. However, we also have examined regions of parameter space where the degenerate states are irregular. A method is proposed that permits one to resolve between degenerate irregular states. It consists of low-temperature expansion in successively larger local clusters or fragments of the allowed zero-temperature states. In principle one need have no a priori knowledge of the symmetry of the zero-temperature state. However, there results a packing problem that involves maximizing the number of clusters with optimal free-energy density. In some cases we have been able to solve this problem, while for other parts of the phase diagram we have made conjectures that have yet to be confirmed by rigorous calculations.

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