Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model

Abstract

We study inequivalence of canonical and microcanonical ensembles in the mean-field Blume-Emery-Griffiths model. This generalizes previous results obtained for the Blume-Capel model. The phase diagram strongly depends on the value of the biquadratic exchange interaction K, the additional feature present in the Blume-Emery-Griffiths model. At small values of K, as for the Blume-Capel model, lines of first and second order phase transitions between a ferromagnetic and a paramagnetic phase are present, separated by a tricritical point whose location is different in the two ensembles. At higher values of K the phase diagram changes substantially, with the appearance of a triple point in the canonical ensemble which does not find any correspondence in the microcanonical ensemble. Moreover, one of the first order lines that starts from the triple point ends in a critical point, whose position in the phase diagram is different in the two ensembles. This line separates two paramagnetic phases characterized by a different value of the quadrupole moment. These features were not previously studied for other models and substantially enrich the landscape of ensemble inequivalence, identifying new aspects that had been discussed in a classification of phase transitions based on singularity theory. Finally, we discuss ergodicity breaking, which is highlighted by the presence of gaps in the accessible values of magnetization at low energies: it also displays new interesting patterns that are not present in the Blume-Capel model.

arXiv commentSmall additions in the Conclusions

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• A large deviation perspective on ratio observables in reset processes: robustness of rate functions
• Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of external magnetic field on a complete graph
• Specific Features of Phase States of a Diluted 2D Magnet with Frustration
• Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions
• Bad metal and negative compressibility transitions in a two-band Hubbard model
• Phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction