Scattering Properties of Paramagnetic Ground States in the Three-Dimensional Random-Field Ising Model

TL;DR

This paper investigates the scattering properties of paramagnetic ground states in the three-dimensional random-field Ising model, revealing fractal interfaces and a cusp singularity in the correlation function at short distances.

Contribution

It introduces an efficient graph-cut method to study the ground states and characterizes the scattering properties of paramagnetic states in the RFIM.

Findings

Paramagnetic states form correlated domains with fractal interfaces.

Short-distance correlation functions exhibit a cusp singularity.

The study provides insights into the morphology of disordered magnetic systems.

Abstract

We study the ground-state (T = 0) morphologies in the d = 3 random-field Ising model (RFIM) using a computationally efficient graph-cut method. We focus on paramagnetic states which arise for disorder strengths \Delta > \Delta c, where \Delta c is the critical disorder strength at T = 0. These paramagnetic states consist of correlated "domains" of up and down spins which are separated by rough, fractal interfaces. They show novel scattering properties with a cusp singularity in the correlation function at short distances.