## 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 for both 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 nonlinear interactions is also studied by microcanonical Monte Carlo simulations in two dimensions to see how this model behaves in comparison with the spherical model.

Original language | English |
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Article number | P08024 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2011 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2011 Aug 1 |

## Keywords

- classical Monte Carlo simulations
- classical phase transitions (theory)
- phase diagrams (theory)
- rigorous results in statistical mechanics

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty