Correlated Initial Conditions in Directed Percolation

TL;DR

This paper studies how correlated initial conditions affect the time evolution of critical directed percolation, revealing that the density of active sites follows a power law with an exponent depending on initial correlations, confirmed by simulations and field theory.

Contribution

It introduces a detailed analysis of correlated initial states in directed percolation and derives the dependence of the growth exponent on initial correlation parameters.

Findings

The active site density follows a power law over time.

The exponent varies continuously with initial correlation strength.

Numerical results align with field-theoretical predictions.

Abstract

We investigate the influence of correlated initial conditions on the temporal evolution of a (d+1)-dimensional critical directed percolation process. Generating initial states with correlations <s_i*s_{i+r}>~r^(sigma-d) we observe that the density of active sites in Monte-Carlo simulations evolves as rho(t)~t^kappa. The exponent kappa depends continuously on sigma and varies in the range -beta/nu_{||}<=kappa<=eta. Our numerical results are confirmed by an exact field-theoretical renormalization group calculation.