Attacks and Infections in Percolation Processes

TL;DR

This paper investigates the scaling behavior of attacks and infections in percolation processes, providing critical exponents for different transitions and validating results with numerical data.

Contribution

It introduces a field-theoretic approach to analyze attacks and infections in percolation, calculating critical exponents for tricritical and ordinary percolation.

Findings

Critical exponents for tricritical percolation calculated in mean-field theory.

Critical exponents for ordinary percolation obtained to 1-loop order.

Results align well with existing numerical data.

Abstract

We discuss attacks and infections at propagating fronts of percolation processes based on the extended general epidemic process. The scaling behavior of the number of the attacked and infected sites in the long time limit at the ordinary and tricritical percolation transitions is governed by specific composite operators of the field-theoretic representation of this process. We calculate corresponding critical exponents for tricritical percolation in mean-field theory and for ordinary percolation to 1-loop order. Our results agree well with the available numerical data.