Replica-symmetry breaking for directed polymers

TL;DR

This paper investigates the complex phase-space structure of directed polymers on large lattices, revealing behaviors akin to replica-symmetry breaking and ultrametricity, with implications for understanding disordered systems.

Contribution

It provides the first large-scale numerical analysis of replica-symmetry breaking phenomena in directed polymers, including phase transition behavior and ultrametricity.

Findings

One ensemble shows ferromagnet-like behavior.

Two ensembles exhibit replica-symmetry breaking indications.

Results support complex phase-space structures in directed polymers.

Abstract

Directed polymers on 1+1 dimensional lattices coupled to a heat bath at temperature $T$ are studied numerically for three ensembles of the site disorder. In particular correlations of the disorder as well as fractal patterning are considered. Configurations are directly sampled in perfect thermal equilibrium for very large system sizes with up to $N=L^2= 32768 \times 32768 \approx 10^{9}$ sites. The phase-space structure is studied via the distribution of overlaps and hierarchical clustering of configurations. One ensemble shows a simple behavior like a ferromagnet. The other two ensembles exhibit indications for complex behavior reminiscent of multiple replica-symmetry breaking. Also results for the ultrametricity of the phase space and the phase transition behavior of $P(q)$ when varying the temperature $T$ are studied. In total, the present model ensembles offer convenient numerical accesses to comprehensively studying complex behavior.