Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems

TL;DR

This paper introduces a universal relation linking static and dynamic corrections in percolating systems, supported by a cluster-resolved scaling theory and extensive simulations, enhancing understanding of critical transport phenomena.

Contribution

It presents a novel universal exponent relation connecting static and dynamic corrections in percolation, derived from a unified cluster-resolved scaling theory.

Findings

Derived a universal correction exponent relation at criticality.

Validated the theory with extensive simulations on a square lattice.

Numerically determined static and dynamic correction exponents.

Abstract

For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our derivation is based on a cluster-resolved scaling theory unifying the scaling of both the cluster size distribution and the dynamics of a random walker. We corroborate our theoretical approach by extensive simulations for a site percolating square lattice and numerically determine both the static and dynamic correction exponents.