Ensemble dependence of the critical behavior of a system with long-range interaction and quenched randomness

TL;DR

This paper investigates a hybrid spin model combining Ising and BEG spins with long-range interactions, revealing complex phase behaviors dependent on spin concentration and ensemble type.

Contribution

It introduces a novel hybrid model with quenched randomness and analyzes its phase behavior across different ensembles, highlighting unusual and rich phase portraits.

Findings

Phase portraits vary with Ising spin concentration.

Distinct behaviors observed in canonical and microcanonical ensembles.

Rich and unusual phase transition phenomena identified.

Abstract

We propose a hybrid model governed by the Blume-Emery-Griffiths (BEG) Hamiltonian with a mean-field-like interaction, where the spins are randomly quenched such that some of them are "pure" Ising and the others admit the BEG set of states. It is found, by varying the concentration of the Ising spins, that the model displays different phase portraits in concentration-temperature parameter space, within the canonical and the microcanonical ensembles. Phenomenological indications that these portraits are rich and rather unusual are provided.