Global Persistence in Directed Percolation

TL;DR

This paper studies the global persistence exponent in directed percolation at criticality, calculating its value and corrections using renormalization group methods, and establishing it as a new independent critical exponent.

Contribution

It introduces the global persistence exponent as a new independent critical exponent and computes its first-order epsilon correction using combined analytical techniques.

Findings

Global persistence exponent theta_p=2 in d<4

First-order epsilon correction to theta_p computed

Comparison with simulations confirms theoretical predictions

Abstract

We consider a directed percolation process at its critical point. The probability that the deviation of the global order parameter with respect to its average has not changed its sign between 0 and t decays with t as a power law. In space dimensions d<4 the global persistence exponent theta_p that characterizes this decay is theta_p=2 while for d<4 its value is increased to first order in epsilon = 4-d. Combining a method developed by Majumdar and Sire with renormalization group techniques we compute the correction to theta_p to first order in epsilon. The global persistence exponent is found to be a new and independent exponent. We finally compare our results with existing simulations.