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arXiv · 1512.06986

The free energy in a class of quantum spin systems and interchange processes

J. E. Björnberg
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Abstract

We study a class of quantum spin systems in the mean-field setting of the complete graph. For spin $S=\tfrac12$ the model is the Heisenberg ferromagnet, for general spin $S\in\tfrac12\mathbb{N}$ it has a probabilistic representation as a cycle-weighted interchange process. We determine the free energy and the critical temperature (recovering results by Tóth and by Penrose when $S=\tfrac12$). The critical temperature is shown to coincide (as a function of $S$) with that of the $q=2S+1$ state classical Potts model, and the phase transition is discontinuous when $S\geq1$.

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J. E. Björnberg. 2015-12-22. The free energy in a class of quantum spin systems and interchange processes. https://doi.org/10.1063/1.4959238

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