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