Diffusion in disordered lattices and related Heisenberg ferromagnets

TL;DR

This paper investigates how particles diffuse in disordered lattices and related ferromagnetic systems using a quantum spin analogy, revealing different decay behaviors in various disordered structures.

Contribution

It introduces an exact method to analyze correlation functions in disordered lattices via quantum spin representations, applied to diluted chains and percolation clusters.

Findings

Density fluctuations decay as stretched exponentials in diluted chains.

Anomalous power law decay is conjectured for percolation clusters.

The approach provides insights into diffusion in disordered magnetic systems.

Abstract

We study the diffusion of classical hard-core particles in disordered lattices within the formalism of a quantum spin representation. This analogy enables an exact treatment of non-instantaneous correlation functions at finite particle densities in terms of single spin excitations in disordered ferromagnetic backgrounds. Applications to diluted chains and percolation clusters are discussed. It is found that density fluctuations in the former exhibit a stretched exponential decay while an anomalous power law asymptotic decay is conjectured for the latter.