Directed percolation with a single defect site

TL;DR

This paper investigates how a single defect site affects the critical behavior of the contact process, proposing that survival probability decays as a stretched exponential, which explains previous non-universal scaling observations.

Contribution

It introduces a new decay form for survival probability in the contact process with a defect site, challenging the previously assumed power-law decay.

Findings

Survival probability decays as a stretched exponential.

Explains the non-universal scaling behavior observed in previous studies.

Provides a theoretical framework for defect site effects in contact processes.

Abstract

In a recent study [arXiv:1011.3254] the contact process with a modified creation rate at a single site was shown to exhibit a non-universal scaling behavior with exponents varying with the creation rate at the special site. In the present work we argue that the survival probability decays according to a stretched exponential rather than a power law, explaining previous observations.