Directed Polymers on a Factorized Disorder Landscape

TL;DR

This paper investigates a directed polymer model with a specific factorized disorder, revealing two new universality classes and a phase transition between distinct scaling behaviors, supported by numerical analysis.

Contribution

It introduces a novel disorder structure in the directed polymer model and uncovers two universality classes along with a phase transition between them.

Findings

Two new universality classes depending on lattice geometry

Existence of a phase transition between two scaling phases

Numerical results support the understanding of exponents in both phases

Abstract

We study the Directed Polymer model subject to a particular form of disorder, $\eta(x,t)=\eta_X(x) \eta_T(t)$, recently proposed in biological applications. We find that two new universality classes arise, depending on the the lattice geometry. Using an intermediate model linking the two different orientations continuously, we find that there is a phase transition separating two distinct scaling phases. For both phases we get a reasonable understanding of the nature and values of the exponents, corroborated with numerical results.