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

TL;DR

This paper investigates how finite-size effects influence the stationary state near the phase transition in directed percolation above the upper critical dimension, revealing modified scaling laws.

Contribution

It analytically derives and numerically confirms new finite-size scaling forms for directed percolation above the upper critical dimension.

Findings

Finite-size scaling is modified above the upper critical dimension.

Derived scaling forms are confirmed by numerical simulations.

Standard finite-size scaling fails 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.