Scaling of local persistence in the disordered contact process

Abstract

We study the time-dependence of the local persistence probability during a non-stationary time evolution in the disordered contact process in $d=1,2$, and $3$ dimensions. We present a method for calculating the persistence with the strong-disorder renormalization group (SDRG) technique, which we then apply in the critical point analytically for $d=1$ and numerically for $d=2,3$. According to the results, the average persistence decays at late times as an inverse power of the logarithm of time, with a universal, dimension-dependent generalized exponent. For $d=1$, the distribution of sample-dependent local persistences is shown to be characterized by a universal limit distribution of effective persistence exponents. By a phenomenological approach of rare-region effects in the active phase, we obtain a non-universal algebraic decay of the average persistence for $d=1$, and enhanced power laws for $d>1$. As an exception, for randomly diluted lattices, the algebraic decay holds to be valid for $d>1$, which is explained by the contribution of dangling ends. Results on the time-dependence of average persistence are confirmed by Monte Carlo simulations. We also prove the equivalence of the persistence with a return probability, a valuable tool for the argumentations.

arXiv comment10 pages, 7 figures

References in corpus (36)

• Universality classes in nonequilibrium lattice systems
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Strong disorder RG approach of random systems
• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• Nontrivial Exponent for Simple Diffusion
• Random Walkers in 1-D Random Environments: Exact Renormalization Group Analysis
• Persistence in Nonequilibrium Systems
• Strong disorder fixed point in absorbing state phase transitions
• Critical Dynamics of the Contact Process with Quenched Disorder
• Persistent spins in the linear diffusion approximation of phase ordering and zeros of stationary gaussian processes
• Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments
• Infinite-randomness critical point in the two-dimensional disordered contact process
• Absorbing state phase transitions with quenched disorder
• Critical behavior and Griffiths effects in the disordered contact process
• Renormalization group study of the two-dimensional random transverse-field Ising model
• Strong Disorder RG approach - a short review of recent developments
• Infinite disorder scaling of random quantum magnets in three and higher dimensions
• Critical Properties of Random Quantum Potts and Clock Models
• Criticality and quenched disorder: rare regions vs. Harris criterion
• Renormalization group study of random quantum magnets
• Numerical Study of Local and Global Persistence in Directed Percolation
• Anomalous diffusion in disordered media and random quantum spin chains
• Exact persistence exponent for the $2d$-diffusion equation and related Kac polynomials
• Exact Results on Sinai's Diffusion
• Persistence at the onset of spatiotemporal intermittency in coupled map lattices
• Monte-Carlo simulations of the clean and disordered contact process in three dimensions
• Numerical study of persistence in systems with absorbing states
• Exact Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift
• Local Persistence in the Directed Percolation Universality Class
• The one-dimensional contact process: duality and renormalisation
• Local persistence in directed percolation
• 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
• Dynamic Phase Transition in Prisoner's Dilemma on a Lattice with Stochastic Modifications
• Extinction transition in stochastic population dynamics in a random, convective environment
• Distribution of dynamical quantities in the contact process, random walks, and quantum spin chains in random environments

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