Correlated Initial Conditions in Directed Percolation

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.

10 pages, RevTeX, including 5 encapsulated postscript figures

References in corpus (4)

• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Generalized Scaling for Models with Multiple Absorbing States
• Series expansions of the percolation probability for directed square and honeycomb lattices
• Intermittency Studies in Directed Bond Percolation

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