Further results on the free energy of the random field Ising chain in the case of centered disorder

TL;DR

This paper extends the understanding of the free energy behavior in the random field Ising chain with centered disorder, providing a more general expansion and identifying key constants in the model.

Contribution

It generalizes previous results to cases with finite second moments and determines an unknown constant in the free energy expansion.

Findings

Extended the free energy expansion to finite second moments.

Identified the first non-universal constant in the free energy expansion.

Provided a more comprehensive understanding of the model's asymptotic behavior.

Abstract

We study the expansion of the limiting free energy density of the random field Ising chain with centered IID disorder and homogeneous coupling parameter, when the latter goes to infinity. We extend the first order result of [Collin, 2025] to the general case of finite second moment. Furthermore, we identify the value of the unknown constant appearing in the main theorem of [Collin, Giacomin, Greenblatt, Hu, 2025], which is the first non-universal constant in the expansion of the limiting free energy density.