Monte Carlo studies of extensions of the Blume-Emery-Griffiths model

TL;DR

This paper extends the Blume-Emery-Griffiths model to two components, investigates its phase diagram via Monte Carlo simulations, and explores applications to superconductors, cold atoms, and Fermi mixtures, revealing complex phase behaviors.

Contribution

The paper introduces a two-component BEG model and analyzes its phase diagram using Monte Carlo methods, including effects of trapping potentials and external fields.

Findings

Rich phase diagram with coexistence of superconductivity and magnetism

No true phase separation in trapped BEG model, only crossover behavior

Predictions for cold atom mixtures to guide future experiments

Abstract

We extend the Blume-Emery-Griffiths (BEG) model to a two-component BEG model in order to study 2D systems with two order parameters, such as magnetic superconductors or two-component Bose-Einstein condensates. The model is investigated using Monte Carlo simulations, and the temperature-concentration phase diagram is determined in the presence and absence of an external magnetic field. This model exhibits a rich phase diagram, including a second-order transition to a phase where superconductivity and magnetism coexist. Results are compared with experiments on Cerium-based heavy-fermion superconductors. To study cold atom mixtures, we also simulate the BEG and two-component BEG models with a trapping potential. In the BEG model with a trap, there is no longer a first order transition to a true phase-separated regime, but a crossover to a kind of phase-separated region. The relation with imbalanced fermi-mixtures is discussed. We present the phase diagram of the two-component BEG model with a trap, which can describe boson-boson mixtures of cold atoms. Although there are no experimental results yet for the latter, we hope that our predictions could help to stimulate future experiments in this direction.