Effect of Dilution on Spinodals and Pseudospinodals

TL;DR

This paper examines how quenched dilution influences critical and spinodal points in mean-field and long-range Ising models, revealing differences from short-range models and implications for metastability and nucleation.

Contribution

It demonstrates that dilution effects in mean-field models are not governed by the Harris criterion and differ from short-range models at the upper critical dimension.

Findings

Dilution affects spinodal points differently than critical points.

Mean-field behavior diverges from $d=4$ nearest neighbor models.

Results inform understanding of metastability in disordered systems.

Abstract

We investigate the effect of quenched dilution on the critical and spinodal points in the infinite range (mean-field) and long-range (near-mean-field) Ising model. We find that unlike the short-range Ising model, the effect of the dilution is not simply related to the divergence of the specific heat, i.e., the Harris criterion. We also find the mean-field behavior differs from that of $d=4$ (upper critical dimension) nearest neighbor model at the critical point. These results are an important first step for understanding the effect of the spinodal on the nucleation process as well as the properties of the metastable state in systems of considerable interest in material science, geophysics, and econophysics which in general have defects.