Percolation of finite-sized objects on a lattice

TL;DR

This paper investigates how finite-sized objects percolate on 2D and 3D lattices, revealing a well-defined threshold, critical exponents, and implications for transport in impurity-doped oxides.

Contribution

It introduces a model for finite-sized object percolation, estimates magnetic polaron sizes, and determines critical exponents, advancing understanding of transport phenomena in complex materials.

Findings

Identified a well-defined percolation threshold.

Estimated magnetic polaron sizes relevant to transport.

Derived two critical exponents characterizing the universality class.

Abstract

We study the percolation of FINITE-SIZED objects on two- and three-dimensional lattices. Our motivation stems, on one hand from some recent interesting experimental results on transport properties of impurity-doped oxide perovskites and on the other hand from the theoretical appeal that this problem presents. Our system exhibits a well-defined percolation threshold. We estimate the size of magnetic polarons, believed to be the carriers of the abovementioned transport. We have also obtained two critical exponents for our model, which characterize its universality class.