Density of critical clusters in strips of strongly disordered systems

TL;DR

This paper investigates the distribution and density profiles of critical clusters in disordered systems, using numerical and analytical methods to verify scaling and conformal predictions.

Contribution

It provides new numerical estimates for critical exponents and confirms the applicability of conformal formulas to disordered systems' cluster density profiles.

Findings

Density profiles follow scaling predictions near boundaries.

Conformal formulas accurately describe cluster densities in the Potts model.

Critical exponents are estimated with high precision.

Abstract

We consider two models with disorder dominated critical points and study the distribution of clusters which are confined in strips and touch one or both boundaries. For the classical random bond Potts model in the large-q limit we study optimal Fortuin-Kasteleyn clusters by combinatorial optimization algorithm. For the random transverse-field Ising chain clusters are defined and calculated through the strong disorder renormalization group method. The numerically calculated density profiles close to the boundaries are shown to follow scaling predictions. For the random bond Potts model we have obtained accurate numerical estimates for the critical exponents and demonstrated that the density profiles are well described by conformal formulae.