# Dimensional reduction and its breakdown in the driven random field O(N) model

## TL;DR

This paper investigates the critical behavior of the driven random field O(N) model at zero temperature, revealing the breakdown of dimensional reduction in low dimensions through non-perturbative renormalization group analysis.

## Contribution

It introduces a non-perturbative RG approach to analyze the driven random field O(N) model and identifies the conditions under which dimensional reduction fails.

## Key findings

- Dimensional reduction holds in high dimensions but breaks down in low dimensions.
- Critical exponents are calculated near three dimensions.
- The range of N where dimensional reduction breaks down is determined.

## Abstract

The critical behavior of the random field $O(N)$ model driven at a uniform velocity is investigated at zero-temperature. From naive phenomenological arguments, we introduce a dimensional reduction property, which relates the large-scale behavior of the $D$-dimensional driven random field $O(N)$ model to that of the $(D-1)$-dimensional pure $O(N)$ model. This is an analogue of the dimensional reduction property in equilibrium cases, which states that the large-scale behavior of $D$-dimensional random field models is identical to that of $(D-2)$-dimensional pure models. However, the dimensional reduction property breaks down in low enough dimensions due to the presence of multiple meta-stable states. By employing the non-perturbative renormalization group approach, we calculate the critical exponents of the driven random field $O(N)$ model near three-dimensions and determine the range of $N$ in which the dimensional reduction breaks down.