Phase transitions in full counting statistics of free fermions and directed polymers

TL;DR

This paper investigates phase transitions in the statistical behavior of free fermions and directed polymers, revealing a continuous transition related to the merging of empty regions in the limit shape under strong external potential.

Contribution

It introduces an exact mapping between directed polymers and free fermions to analyze phase transitions in their configurations.

Findings

Identifies a continuous phase transition in directed polymers under strong potential.

Shows the merging of empty regions in the limit shape signifies the transition.

Provides a theoretical framework connecting fermions and polymers for phase transition analysis.

Abstract

We consider directed polymers in 1+1 spatial dimension under action of an external repulsive potential along a line. Using the exact mapping onto imaginary time evolution of free fermions we find that for sufficiently strong potential the system of polymers undergoes a continuous configurational phase transition. The transition corresponds to merging empty regions in the dominant limit shape.