Finite-size scaling of directed percolation above the upper critical dimension

Abstract

We consider analytically as well as numerically the finite-size scaling behavior in the stationary state near the non-equilibrium phase transition of directed percolation within the mean field regime, i.e., above the upper critical dimension. Analogous to equilibrium, usual finite-size scaling is valid below the upper critical dimension, whereas it fails above. Performing a momentum analysis of associated path integrals we derive modified finite-size scaling forms of the order parameter and its higher moments. The results are confirmed by numerical simulations of corresponding high-dimensional lattice models.

arXiv comment4 pages, one figure

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• Tricritical directed percolation
• Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks
• Rare regions and Griffiths singularities at a clean critical point: The five-dimensional disordered contact process
• Finite-size scaling of directed percolation in the steady state
• Equivalence of conditional and external field ensembles in absorbing state phase transitions
• Stochastic spreading processes on a network model based on regular graphs