Successively Thresholded Domain Boundary Roughening Driven by Pinning Centers and Missing Bonds: Hard-Spin Mean-Field Theory Applied to d=3 Ising Magnets

TL;DR

This paper extends hard-spin mean-field theory to study how quenched impurities like pinning centers and missing bonds induce successive thresholding in domain boundary roughening in 3D Ising magnets, revealing universal behavior at high anisotropy.

Contribution

It introduces a novel application of mean-field theory to analyze impurity-induced roughening transitions in three-dimensional Ising models with anisotropy.

Findings

Impurities cause domain boundary roughening with successive threshold transitions.

At high anisotropy, systems reach a universal 'solid-on-solid' limit.

The domain boundary width follows a universal curve with impurity concentration.

Abstract

Hard-spin mean-field theory has recently been applied to Ising magnets, correctly yielding the absence and presence of an interface roughening transition respectively in $d=2$ and $d=3$ dimensions and producing the ordering-roughening phase diagram for isotropic and anisotropic systems. The approach has now been extended to the effects of quenched random pinning centers and missing bonds on the interface of isotropic and anisotropic Ising models in $d=3$. We find that these frozen impurities cause domain boundary roughening that exhibits consecutive thresholding transitions as a function interaction of anisotropy. For both missing-bond and pinning-center impurities, for moderately large values the anisotropy, the systems saturate to the "solid-on-solid" limit, exhibiting a single universal curve for the domain boundary width as a function of impurity concentration.