The random field Ising chain domain-wall structure in the large interaction limit

TL;DR

This paper investigates the structure of spin configurations in a large interaction limit of the random field Ising chain, revealing how disorder influences the configurations and confirming theoretical predictions.

Contribution

It provides a quantitative estimate of the spin configurations' proximity to a disorder-dependent state in the large interaction limit, linking rigorous analysis with prior renormalization group predictions.

Findings

Spin configurations are close to a disorder-dependent configuration at large interactions.

Disorder has a strong effect on the free energy and configurations.

Results confirm previous theoretical predictions using renormalization group methods.

Abstract

We study the configurations of the nearest neighbor Ising ferromagnetic chain with IID centered and square integrable external random field in the limit in which the pairwise interaction tends to infinity. The available free energy estimates for this model show a strong form of disorder relevance, i.e., a strong effect of disorder on the free energy behavior, and our aim is to make explicit how the disorder affects the spin configurations. We give a quantitative estimate that shows that the infinite volume spin configurations are close to one explicit disorder dependent configuration when the interaction is large. Our results confirm predictions on this model obtained in D. S. Fisher, P. Le Doussal and C. Monthus (Phys. Rev. E 2001) by applying the renormalization group method introduced by D. S. Fisher (Phys. Rev. B 1995).