Interface mapping in two-dimensional random lattice models

TL;DR

This paper investigates the interface properties of two disordered lattice models, the random field Ising model and the random bond Potts model, using exact combinatorial optimization to compare their behaviors under varying disorder strengths.

Contribution

It provides an exact computational analysis of interface evolution in two related disordered models, extending understanding of their mapping in finite systems.

Findings

Interfaces show similar evolution patterns with increasing disorder.

Exact solutions reveal differences in interface roughness between models.

Comparison supports continuum mapping validity in finite samples.

Abstract

We consider two disordered lattice models on the square lattice: on the medial lattice the random field Ising model at T=0 and on the direct lattice the random bond Potts model in the large-q limit at its transition point. The interface properties of the two models are known to be related by a mapping which is valid in the continuum approximation. Here we consider finite random samples with the same form of disorder for both models and calculate the respective equilibrium states exactly by combinatorial optimization algorithms. We study the evolution of the interfaces with the strength of disorder and analyse and compare the interfaces of the two models in finite lattices.