C. A. Hooley, P. D. Stevenson
We analyse the Lipkin-Meshkov-Glick model near, but not in, the thermodynamic limit, for arbitrary strengths of the two types of inter-fermion interaction, and at non-zero temperature. We use semiclassical methods to obtain the crossover temperature, T*(V,W), between linear and nonlinear behavior. It is shown that T* typically vanishes logarithmically as the quantum phase transition from the symmetric to the distorted state is approached, except near the quantum tricritical point (V,W)=(0,-epsilon), where it becomes linear. We discuss the relationship of the T* line to those observed in conventional condensed matter systems. These calculations are supplemented by a direct quantum solution near the line V=0. This reveals a quantum singlet phase for large positive W that is not accessible via semi-classical techniques.
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http://arxiv.org/abs/1102.1583
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