Universal scaling behavior of directed percolation around the upper critical dimension

Abstract

In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function of the control parameter and the conjugated field. Additionally to the universal scaling functions, several universal amplitude combinations are considered. We compare our results with those of a renormalization group approach.

arXiv comment19 pages, 8 figures, accepted for publication in J. Stat. Phys

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• Crossover from Isotropic to Directed Percolation
• Scaling behavior of the directed percolation universality class
• Finite-size scaling of directed percolation above the upper critical dimension
• Finite-size scaling of directed percolation in the steady state
• Logarithmic corrections in (4+1)-dimensional directed percolation
• Consensus formation and relative stimulus perception in quality-sensitive, interdependent agent systems
• Transport properties of directed percolation clusters at the upper critical dimension
• Critical and quasicritical behavior in a three-species dynamical model of semi-directed percolation