Ground State Structure of Random Magnets

TL;DR

This paper employs exact optimization to identify all ground states of random-field Ising magnets and dilute antiferromagnets, revealing the structure and entropy contributions of isolated clusters across dimensions.

Contribution

It provides a comprehensive analysis of ground state structures and entropy in RFIM and DAFF using exact methods, highlighting the role of isolated clusters.

Findings

Ground states are composed of isolated clusters embedded in a frozen background.

Positive ground state entropy persists across a broad parameter regime.

Both 2D and 3D systems exhibit similar cluster-induced properties.

Abstract

Using exact optimization methods, we find all of the ground states of +/- h random-field Ising magnets (RFIM) and of dilute antiferromagnets in a field (DAFF). The degenerate ground states are usually composed of isolated clusters (two-level systems) embedded in a frozen background. We calculate the paramagnetic response (sublattice response) and the ground state entropy for the RFIM (DAFF) due to these clusters. In both two and three dimensions there is a broad regime in which these quantities are strictly positive, even at irrational values of h/J (J is the exchange constant).