The field theory approach to percolation processes
By H. Janssen, Uwe Claus Täuber. 2004
159 citations recorded by the source corpus.
Abstract We review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous non-equilibrium active to absorbing state phase transitions whose asymptotic features are governed, respectively, by the directed (DP) and dynamic isotropic percolation (dIP) universality classes. We discuss the construction of a field theory representation for these Markovian stochastic processes based on fundamental phenomenological considerations, as well as from a specific microscopic reaction-diffusion model realization. Subsequently we explain how dynamic renormalization group (RG) methods can be applied to obtain the universal properties near the critical point in an expansion about the upper critical dimensions dc = 4 (DP) and 6 (dIP). We provide a detailed overview of results for critical exponents, scaling functions, crossover phenomena, finite-size scaling, and also briefly comment on the influence of long-range spreading, the presence of a boundary, multispecies generalizations, coupling of the order parameter to other conserved modes, and quenched disorder.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/6fe25984707bd655e8590b53f1e720184b2cdae0
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In Condensed Matter Physics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Stochastic population dynamics in spatially extended predator–prey systems (2017, background): “that captures the universal scaling properties of critical directed percolation [96, 93, 60].”