# New loop expansion for the Random Magnetic Field Ising Ferromagnets at zero temperature

## TL;DR

This paper introduces a novel loop expansion method for the zero-temperature Random Field Ising Model, providing a more suitable framework for strongly disordered systems and revealing new cubic vertex contributions.

## Contribution

The paper develops a new perturbative loop expansion around the Bethe solution tailored for T=0 disordered systems, differing from the epsilon-expansion and maintaining dimensional reduction validity.

## Key findings

- New cubic vertices in the effective theory
- One-loop corrections reveal additional terms
- Dimensional reduction remains valid at this order

## Abstract

We apply to the Random Field Ising Model at zero temperature (T= 0) the perturbative loop expansion around the Bethe solution. A comparison with the standard epsilon-expansion is made, highlighting the key differences that make the new expansion much more appropriate to correctly describe strongly disordered systems, especially those controlled by a T = 0 RG fixed point. This new loop expansion produces an effective theory with cubic vertices. We compute the one-loop corrections due to cubic vertices, finding new terms that are absent in the epsilon-expansion. However, these new terms are subdominant with respect to the standard, supersymmetric ones, therefore dimensional reduction is still valid at this order of the loop expansion.