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Ensemble equivalence in spin systems with short-range interactions

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Takahashi, Kazutaka and Nishimori, Hidetoshi and Martín Mayor, Víctor (2011) Ensemble equivalence in spin systems with short-range interactions. Journal of statistical mechanics : theory and experiment . ISSN 1742-5468

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Official URL: http://dx.doi.org/10.1088/1742-5468/2011/08/P08024




Abstract

We study the problem of ensemble equivalence in spin systems with short-range interactions under the existence of a first-order phase transition. The spherical model with nonlinear nearest-neighbour interactions is solved exactly both for canonical and microcanonical ensembles. The result reveals apparent ensemble inequivalence at the first-order transition point in the sense that the microcanonical entropy is non-concave as a function of the energy and consequently the specific heat is negative. In order to resolve the paradox, we show that an unconventional saddle point should be chosen in the microcanonical calculation that represents a phase separation. The XY model with non-linear interactions is also studied by microcanonical Monte Carlo simulations in two dimensions to see how this model behaves in comparison with the spherical model.


Item Type:Article
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© 2011 IOP Publishing Ltd and SISSA.

Uncontrolled Keywords:Negative specific-heat; Phase-transitions; Long-range; 1st-order transition; XY-model; Thermodynamics; Inequivalence; Dynamics.
Subjects:Sciences > Physics > Physics-Mathematical models
ID Code:45095
Deposited On:22 Nov 2017 11:45
Last Modified:22 Nov 2017 11:45

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