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arXiv:cond-mat/0110244 · Physica A Statistical Mechanics and its Applications

Microcanonical solution of lattice models with long-range interactions

Julien Barré

Published Mar 1, 2002• 18 citations
arXivHTMLPDF
DOI
10.1016/s0378-4371(01)00657-4

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Motivated by the anisotropic long-range nature of the interactions between cold dipolar atoms or molecules in an optical lattice, we study the anisotropic quantum Heisenberg model with Curie-Weiss-type long-range interactions. Absence of a heat bath in optical lattice experiments suggests a study of this model within the microcanonical ensemble. The microcanonical entropy is calculated analytically and nonequivalence of microcanonical and canonical ensembles is found for a range of anisotropy parameters. From the shape of the entropy it follows that the Curie-Weiss Heisenberg model is indistinguishable from the Curie-Weiss Ising model in canonical thermodynamics, although their microcanonical thermodynamics differs. Qualitatively, the observed features of nonequivalent ensembles are expected to be relevant for long-range quantum spin systems realized in optical lattice experiments.