Replica Bethe ansatz derivation of the GOE Tracy-Widom distribution in one-dimensional directed polymers with free boundary conditions

TL;DR

This paper derives the distribution of free energy fluctuations in 1D directed polymers with free boundaries, showing it follows the universal Tracy-Widom GOE distribution using a replica Bethe ansatz approach.

Contribution

It provides a novel derivation of the Tracy-Widom GOE distribution for directed polymers with free boundary conditions via replica Bethe ansatz.

Findings

Distribution matches Tracy-Widom GOE in the thermodynamic limit

Mapping to quantum boson system enables analytical derivation

Confirms universality of Tracy-Widom distribution in this context

Abstract

The distribution function of the free energy fluctuations in one-dimensional directed polymers with free boundary conditions is derived by mapping the replicated problem to the N-particle quantum boson system with attractive interactions. It is shown that in the thermodynamic limit this function is described by the universal Tracy-Widom distribution of the Gaussian orthogonal ensemble.