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

S. Lubeck·H. -K. Janssen
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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.

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S. Lubeck, H. -K. Janssen. 2005-08-01. Finite-size scaling of directed percolation above the upper critical dimension. https://doi.org/10.1103/physreve.72.016119

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