# On the Ultrametricity Property in Random Field Ising Models

## TL;DR

This paper demonstrates that the ultrametricity property, a hierarchical structure, persists in random field Ising models under small perturbations of the external field, extending understanding of their geometric organization.

## Contribution

It establishes the stability of ultrametricity in random field Ising models with independent disorder when the field strength is a small perturbation.

## Key findings

- Ultrametricity remains valid under small perturbations.
- The property holds for models with independent disorder.
- Results extend the understanding of the geometric structure of these models.

## Abstract

In this paper we show that the ultrametricity property remains valid in random field Ising models with independent disorder whenever the field strength is a small perturbation.