Local Persistence in the Directed Percolation Universality Class

Abstract

We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean field limit. Moreover, we introduce a graded persistence probability that a site does not flip more than n times and demonstrate how local persistence can be studied in seed simulations. Finally, the problem of spatial (as opposed to temporal) persistence is investigated.

LaTeX, 24 pages, 12 figures; references added and corrected, section 4.3 rewritten

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• Dynamic Phase Transition in the Contact Process with Spatial Disorder: Griffths Phase and Complex Persistence Exponents
• Persistence as Order Parameter in Generalized Pair Contact Process with Diffusion
• Noise driven dynamic phase transition in a a one dimensional Ising-like model
• Novel Transition to fully absorbing state without long-range spatial order in Directed Percolation class
• Dynamic Phase Transition from Localized to Spatiotemporal Chaos in Coupled Circle Map with Feedback
• Dynamic Phase Transition in Prisoner's Dilemma on a Lattice with Stochastic Modifications
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• Fluctuations and Persistence in Quantum Diffusion on Regular Lattices
• Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal