Ensemble inequivalence in the Blume-Emery-Griffiths model near a fourth order critical point

TL;DR

This paper investigates the microcanonical phase diagram of the infinite-range Blume-Emery-Griffiths model near a fourth order critical point, revealing differences from the canonical ensemble and extending previous positive-K studies.

Contribution

It provides the first detailed analysis of the microcanonical phase diagram for negative K, highlighting ensemble inequivalence near a fourth order critical point.

Findings

Microcanonical phase diagram differs from canonical one near the critical point.

Fourth order critical point exists at different parameters in microcanonical ensemble.

Distinct features in phase transitions are observed in the microcanonical analysis.

Abstract

The canonical phase diagram of the Blume-Emery-Griffiths (BEG) model with infinite-range interactions is known to exhibit a fourth order critical point at some negative value of the bi-quadratic interaction $K<0$. Here we study the microcanonical phase diagram of this model for $K<0$, extending previous studies which were restricted to positive $K$. A fourth order critical point is found to exist at coupling parameters which are different from those of the canonical ensemble. The microcanonical phase diagram of the model close to the fourth order critical point is studied in detail revealing some distinct features from the canonical counterpart.