# Critical properties of the contact process with quenched dilution

## TL;DR

This study investigates the critical behavior of the contact process on a diluted lattice, revealing its universality class and phase diagram through Monte Carlo simulations and mean-field theory.

## Contribution

It introduces a novel simulation approach combining percolation cluster generation with contact process dynamics on diluted lattices.

## Key findings

- Critical exponents align with the random transverse-field Ising model
- Phase diagram characterized by mean-field theory considering site correlations
- Activated scaling relation confirms dynamic critical behavior

## Abstract

We have studied the critical properties of the contact process on a square lattice with quenched site dilution by Monte Carlo simulations. This was achieved by generating in advance the percolating cluster, through the use of an appropriate epidemic model, and then by the simulation of the contact process on the top of the percolating cluster. The dynamic critical exponents were calculated by assuming an activated scaling relation and the static exponents by the usual power law behavior. Our results are in agreement with the prediction that the quenched diluted contact process belongs to the universality class of the random transverse-field Ising model. We have also analyzed the model and determined the phase diagram by the use of a mean-field theory that takes into account the correlation between neighboring sites.