A Model for Randomly Correlated Deposition

TL;DR

This paper introduces a parametric model for correlated particle deposition on surfaces, exploring how the percolation threshold varies with a parameter k, and discusses applications including magnetic systems and aggregation.

Contribution

It presents a new discrete model incorporating a parameter k to control correlation in particle deposition and analyzes its impact on percolation thresholds and phase transitions.

Findings

Percolation threshold increases with k value.

Model describes phase transition at percolation.

Applicable to magnetic and aggregation systems.

Abstract

A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase transition) when a percolating cluster appears. The parameter k is included in the probability p(k) of particles to stick together and form a cluster on the surface. The case k=1 corresponds to the ordinary 2D percolation on a square lattice. Thus the percolation threshold is controlled by the k-value: the larger k the higher threshold for percolation. The growth model seen from the percolation point of view allows us to describe several interesting applications in addition to irreversible aggregation in the presence of a repulsive force, k>1. For example, the occupied lattice sites might represent regions of specific magnetization in an otherwise disordered medium. Then the whole system is ordered or not according to the concentration of the deposited particles. Object-oriented code is developed for the Monte Carlo part of the calculations.