Finite Size Correction In A Disordered System - A New Divergence

TL;DR

This paper investigates the divergence of finite size correction amplitudes in disordered systems, specifically for directed polymers, revealing a critical divergence characterized by an exponent independent of temperature but dependent on dimensionality.

Contribution

It introduces a new divergence in the finite size correction term for moments of the partition function in disordered directed polymers, highlighting a critical behavior near a specific moment.

Findings

Finite size correction amplitude diverges as (n_c - n)^{-r} on the high temperature side.

The divergence exponent r is independent of temperature.

No divergence occurs on the low temperature side for n > n_c.

Abstract

We show that the amplitude of the finite size correction term for the $n$th moment of the partition function, for randomly interacting directed polymers, diverges (on the high temperature side) as $(n_c - n)^{-r}$, as a critical moment $n_c$ is approached. The exponent $r$ is independent of temperature but does depend on the effective dimensionality. There is no such divergence on the low temperature side ($n>n_c)$.