Interface fluctuations in disordered systems: Universality and non-Gaussian statistics

TL;DR

This paper uses a functional renormalization group approach with a soft-cutoff scheme to study interface fluctuations in disordered systems, confirming the universality of the roughness exponent and exploring non-Gaussian statistics and temperature effects.

Contribution

It introduces a new soft-cutoff scheme in the functional renormalization group analysis, confirming the universality of the roughness exponent and analyzing higher cumulants and temperature effects.

Findings

Confirmed roughness exponent $oxed{ ext{≈} 0.2083 imes ext{epsilon}}$

Demonstrated universality of the roughness exponent

Analyzed generation of higher cumulants and temperature role

Abstract

We employ a functional renormalization group to study interfaces in the presence of a pinning potential in $d=4-\epsilon$ dimensions. In contrast to a previous approach [D.S. Fisher, Phys. Rev. Lett. {\bf 56}, 1964 (1986)] we use a soft-cutoff scheme. With the method developed here we confirm the value of the roughness exponent $\zeta \approx 0.2083 \epsilon$ in order $\epsilon$. Going beyond previous work, we demonstrate that this exponent is universal. In addition, we analyze the generation of higher cumulants in the disorder distribution and the role of temperature as a dangerously irrelevant variable.