Monte Carlo Study of an Inhomogeneous Blume-Capel Model

TL;DR

This study investigates how inhomogeneity affects phase transitions in a classical Blume-Capel model, providing insights into the validity of local density approximation and the nature of critical phenomena.

Contribution

It introduces a spatially varying Blume-Capel model to analyze inhomogeneous phase transitions and compares critical properties for first and second order transitions.

Findings

Inhomogeneity modifies the nature of phase transitions.

The local density approximation's validity varies with transition type.

Critical properties differ between first and second order cases.

Abstract

Systems of particles in a confining potential exhibit a spatially dependent density which fundamentally alters the nature of phase transitions that occur. A specific instance of this situation, which is being extensively explored currently, concerns the properties of ultra-cold, optically trapped atoms. Of interest is how the superfluid-insulator transition is modified by the inhomogeneity, and, indeed, the extent to which a sharp transition survives at all. This paper explores a classical analog of these systems, the Blume-Capel model with a spatially varying single ion anisotropy and/or temperature gradient. We present results both for the nature of the critical properties and for the validity of the "local density approximation" which is often used to model the inhomogeneous case. We compare situations when the underlying uniform transition is first and second order.