Real space renormalisation for reaction-diffusion systems

TL;DR

This paper explores the use of real space renormalisation group methods, originally for quantum systems, to analyze reaction-diffusion models and the contact process, achieving accurate critical parameter estimates.

Contribution

It demonstrates the applicability of quantum-inspired renormalisation techniques to classical reaction-diffusion systems, including exact and approximate results.

Findings

Recovered several exact results for solvable models

Obtained good estimates of critical parameters for the contact process

Validated the method's effectiveness in low-dimensional systems

Abstract

The stationary state of stochastic processes such as reaction-diffusion systems can be related to the ground state of a suitably defined quantum Hamiltonian. Using this analogy, we investigate the applicability of a real space renormalisation group approach, originally developped for quantum spin systems, to interacting particle systems. We apply the technique to an exactly solvable reaction-diffusion system and to the contact process (both in $d=1$). In the former case, several exact results are recovered. For the contact process, surprisingly good estimates of critical parameters are obtained from a small-cell renormalisation.