Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder

TL;DR

This paper compares theoretical replica-symmetric predictions with numerical simulations for two disordered 2D systems, confirming the replica approach's accuracy in describing thermodynamic properties across various disorder strengths.

Contribution

It provides the first detailed quantitative validation of the replica approach for 2D disordered systems by comparing it with numerical simulations.

Findings

Excellent agreement between RBA predictions and simulations across disorder strengths

Mapping of two disordered models enables detailed comparison

Confirms the validity of the replica approach in 2D disordered systems

Abstract

We study the statistics of thermodynamic quantities in two related systems with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in a random potential and the 2-dimensional random bond dimer model. The first system is examined by a replica-symmetric Bethe ansatz (RBA) while the latter is studied numerically by a polynomial algorithm which circumvents slow glassy dynamics. We establish a mapping of the two models which allows for a detailed comparison of RBA predictions and simulations. Over a wide range of disorder strength, the effective lattice stiffness and cumulants of various thermodynamic quantities in both approaches are found to agree excellently. Our comparison provides, for the first time, a detailed quantitative confirmation of the replica approach and renders the planar line lattice a unique testing ground for concepts in random systems.