1997/09/05 by Ronald Dickman, Adriana G. Moreira · 4 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.57.1263
13 pages, revtex, 7 postscript figures
arxiv created 1997/09/05 · openalex publication_date 1998/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the two-dimensional contact process (CP) with quenched disorder (DCP), and determine the static critical exponents \ensuremathβ and \ensuremathν_\ensuremath⊥. The dynamic behavior is incompatible with scaling, as applied to models (such as the pure CP) that have a continuous phase transition to an absorbing state. We find that the survival probability (starting with all sites occupied), for a finite-size system at the critical point, decays according to a power law, as does the off-critical density autocorrelation function. Thus the critical exponent \ensuremathν||, which governs the relaxation time, is undefined, since the characteristic relaxation time is itself undefined. The logarithmic time dependence found in recent simulations of the critical DCP [A. G. Moreira and R. Dickman, Phys. Rev. E 54, R3090 (1996)] is further evidence of violation of scaling. A simple argument based on percolation cluster statistics yields a similar logarithmic evolution.