2002/02/26 by György Szabó, Gyorgy Szabo, Hajnalka Gergely +2
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Biology #Condensed matter physics #Contact process (mathematics) #Critical exponent #Diffusion and Search Dynamics #Directed percolation #Electrical resistivity and conductivity #Homogeneous #Lattice (music) #Mathematics #Monte Carlo method #Percolation (cognitive psychology) #Percolation threshold #Phase transition #Physics #Quantum mechanics #Square lattice #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.65.066111
published as Phys. Rev. E, 65 (2002) 066111. · 6 pages, 7 figures
arxiv created 2002/02/26 · openalex publication_date 2002/06/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time-dependent background, this transition is equivalent to those found in homogeneous systems (i.e., to directed percolation). For frozen backgrounds, the appearance of the Griffiths phase prevents the accurate analysis of this transition. For long times in the subcritical region, the spreading remains localized in compact (rather than ramified) patches, and the average number of occupied sites increases logarithmically in the surviving trials.