Precise Critical Exponents for the Basic Contact Process

TL;DR

This paper accurately calculates critical exponents for the one-dimensional basic contact process using numerical diagonalization and finite-size scaling, providing a method applicable to various stochastic processes.

Contribution

It introduces a precise numerical approach to determine critical exponents in the contact process, emphasizing a simple reasoning for time scale selection in quantum chain formulations.

Findings

High-accuracy estimates of critical exponents achieved

Efficient numerical method with minimal computational effort

Applicable to stochastic processes with finite absorbing states

Abstract

We calculated some of the critical exponents of the directed percolation universality class through exact numerical diagonalisations of the master operator of the one-dimensional basic contact process. Perusal of the power method together with finite-size scaling allowed us to achieve a high degree of accuracy in our estimates with relatively little computational effort. A simple reasoning leading to the appropriate choice of the microscopic time scale for time-dependent simulations of Markov chains within the so called quantum chain formulation is discussed. Our approach is applicable to any stochastic process with a finite number of absorbing states.