Universal scaling behavior of directed percolation around the upper critical dimension

TL;DR

This paper investigates the universal scaling behavior of directed percolation near its upper critical dimension, providing numerical analysis of key quantities and comparing results with renormalization group predictions.

Contribution

It offers a detailed numerical study of steady state scaling in directed percolation and compares universal amplitude ratios with theoretical renormalization group results.

Findings

Numerical determination of order parameter, fluctuations, and susceptibility.

Identification of universal scaling functions and amplitude combinations.

Comparison confirming consistency with renormalization group predictions.

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.