Glassy Solutions of the Kardar-Pasrisi-Zhang Equation

TL;DR

This paper demonstrates that the strong-coupling limit of the KPZ equation exhibits glassy solutions in dimensions greater than four, characterized by persistent surface features and a delta function in the height correlation function.

Contribution

It provides a novel solution to the mode-coupling equations for the KPZ equation in high dimensions, revealing glassy behavior and specific correlation features.

Findings

Dynamic exponent z equals 2 for d>4

Presence of a delta function in the height correlation function

Amplitude of the delta function vanishes as d approaches 4

Abstract

It is shown that the mode-coupling equations for the strong-coupling limit of the KPZ equation have a solution for d>4 such that the dynamic exponent z is 2 (with possible logarithmic corrections) and that there is a delta function term in the height correlation function <h(k,w)h^*(k,w)> = (A/k^{d+4-z}) \delta(w/k^z) where the amplitude A vanishes as d -> 4. The delta function term implies that some features of the growing surface h(x,t) will persist to all times, as in a glassy state.