Universality and Crossover of Directed Polymers and Growing Surfaces

TL;DR

This paper investigates the universality of KPZ surfaces and directed polymers across different lattice types and disorder distributions, revealing a universal crossover behavior and crossover exponent, with analytical and numerical support.

Contribution

It demonstrates that universality applies to these models despite recent conflicting results and identifies a universal crossover exponent of 1/2 in low-dimensional limits.

Findings

Universality holds for KPZ surfaces and directed polymers across various lattices.

A slow power-law crossover toward universal exponents is observed.

The crossover exponent is analytically and numerically found to be 1/2 in 1+epsilon dimensions.

Abstract

We study KPZ surfaces on Euclidean lattices and directed polymers on hierarchical lattices subject to different distributions of disorder, showing that universality holds, at odds with recent results on Euclidean lattices. Moreover, we find the presence of a slow (power-law) crossover toward the universal values of the exponents and verify that the exponent governing such crossover is universal too. In the limit of a 1+epsilon dimensional system we obtain both numerically and analytically that the crossover exponent is 1/2.