The effects of disorder on Harris-criterion violating percolation

TL;DR

This study uses computer simulations to investigate how impurities affect the critical behavior of protected percolation systems that violate the Harris criterion, revealing dimension-dependent stability of critical exponents.

Contribution

It demonstrates that impurities alter critical exponents in three-dimensional protected percolation, while two-dimensional systems remain unaffected, highlighting dimension-specific effects.

Findings

Critical exponents in 3D protected percolation change with impurities.

2D percolation exponents are stable against impurities.

Impurities influence critical behavior differently depending on system dimension.

Abstract

We present the results of computer simulations on a class of percolative systems, called protected percolation, that violates the Harris criterion. The Harris criterion states whether the critical behavior at a phase transition from a disordered state to an ordered state will be altered by impurities. We have incorporated impurities into our simulations to test whether the critical exponents for protected percolation are altered by impurities. We find that the critical exponents for three-dimensional protected percolation simulations indeed change with impurities in the form of missing sites and immortal sites. On the other hand, the critical exponents for both standard percolation and protected percolation in two dimensions are stable against impurities.