Uniqueness of zero-temperature metastate in disordered Ising ferromagnets

TL;DR

This paper proves that in disordered ferromagnetic Ising models, all zero-temperature metastates are trivial, significantly constraining the possible ground state configurations and impacting the understanding of these systems.

Contribution

It establishes the triviality of zero-temperature metastates in disordered ferromagnetic Ising models, providing new insights into their ground state structure.

Findings

All zero-temperature metastates are trivial in these models.

The result restricts the possible ground state configurations.

Connections to first-passage and random surface models are discussed.

Abstract

We study ground states of Ising models with random ferromagnetic couplings, proving the triviality of all zero-temperature metastates. This unexpected result sheds a new light on the properties of these systems, putting strong restrictions on their possible ground state structure. Open problems related to existence of interface-supporting ground states are stated and an interpretation of the main result in terms of first-passage and random surface models in a random environment is presented.