Dimensional reduction in driven disordered systems

TL;DR

This paper explores how driven disordered systems exhibit a form of dimensional reduction similar to equilibrium systems, but this reduction can break down due to nonanalytic disorder effects, with implications for roughness behavior.

Contribution

It provides a detailed functional renormalization group analysis revealing conditions under which dimensional reduction holds or breaks down in driven disordered systems.

Findings

Dimensional reduction applies to single-component systems but not multi-component systems.

Nonanalytic behavior in disorder cumulants causes breakdown of dimensional reduction.

Roughness exponent matches reduction predictions for single-component systems.

Abstract

We investigate the critical behavior of disordered systems transversely driven at a uniform and steady velocity. An intuitive argument predicts that the long-distance physics of $D$-dimensional driven disordered systems at zero temperature is the same as that of the corresponding $(D-1)$-dimensional pure systems in thermal equilibrium. This result is analogous to the well-known dimensional reduction property in thermal equilibrium, which states the equivalence between $D$-dimensional disordered systems and $(D-2)$-dimensional pure systems. To clarify the condition that the dimensional reduction holds, we perform the functional renormalization group analysis of elastic manifolds transversely driven in random media. We argue that the nonanalytic behavior in the second cumulant of the renormalized disorder leads to the breakdown of the dimensional reduction. We further found that the roughness exponent is equal to the dimensional reduction value for the single component case, but it is not for the multi-component cases.