Scaling of fluctuation for Directed polymers with random interaction

TL;DR

This paper investigates the phase transition behavior of directed polymers with random interactions across different dimensions and chain numbers, using finite size scaling to identify disorder-induced transitions and confirming previous theoretical results.

Contribution

It introduces a finite size scaling approach to analyze the binding-unbinding transition in directed polymers with randomness, extending understanding across multiple cases.

Findings

Existence of a disorder-induced transition confirmed

Finite size scaling form applicable across cases

Exponents match previous renormalization group results

Abstract

Using a finite size scaling form for reunion probability, we show numerically the existence of a binding-unbinding transition for Directed polymers with random interaction. The cases studied are (A1) two chains in 1+1 dimensions, (A2) two chains in 2+1 dimensions and (B) three chains in 1+1 dimensions. A similar finite size scaling form for fluctuation establishes a disorder induced transition with identical exponents for cases A2 and B. The length scale exponents in all the three cases are in agreement with previous exact renormalization group results.