Directed Polymers and Interfaces in Disordered Media

TL;DR

This paper develops a field theory approach for directed polymers and interfaces in disordered media, deriving a series representation for free energy and analyzing the structure of field space, confirming known exponents.

Contribution

It introduces a novel series representation for the averaged free energy and analyzes the field space structure for polymers and interfaces at finite temperature.

Findings

Derived a series representation for the averaged free energy.

Analyzed the field space structure using saddle-point equations.

Confirmed the wandering exponent for interfaces as (4-d)/2.

Abstract

We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the model contribute. The structure of field space is analysed for polymers and interfaces at finite temperature using the saddle-point equations derived from each integer moments of the partition function. For the case of an interface we obtain the wandering exponent $\xi= (4-d)/2$, also obtained by the conventional replica method for the replica symmetric scenario.