# On the critical exponent $\alpha$ of the 5D random-field Ising model

## TL;DR

This paper estimates the critical exponent alpha of the specific heat in the 5D random-field Ising model using zero-temperature simulations, supporting the idea of dimensional reduction restoration at five dimensions.

## Contribution

It provides a new numerical estimate of alpha that aligns with hyperscaling relations, offering evidence for dimensional reduction in the 5D RFIM.

## Key findings

- Estimated alpha = 0.12(2) from simulations
- Results support restoration of dimensional reduction at D=5
- Consistent with hyperscaling relation predictions

## Abstract

We present a complementary estimation of the critical exponent $\alpha$ of the specific heat of the 5D random-field Ising model from zero-temperature numerical simulations. Our result $\alpha = 0.12(2)$ is consistent with the estimation coming from the modified hyperscaling relation and provides additional evidence in favor of the recently proposed restoration of dimensional reduction in the random-field Ising model at $D = 5$.