Publication
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Paper

Survival probability and field theory in systems with absorbing states

View publication

Abstract

An important quantity in the analysis of systems with absorbing states is the survival probability [Formula Presented], the probability that an initial localized seed of particles has not completely disappeared after time [Formula Presented]. At the transition into the absorbing phase, this probability scales for large [Formula Presented] like [Formula Presented]. It is not at all obvious how to compute [Formula Presented] in continuous field theories, where [Formula Presented] is strictly unity for all finite [Formula Presented]. We propose here an interpretation for [Formula Presented] in field theory and devise a practical method to determine it analytically. The method is applied to field theories representing absorbing-state systems in several distinct universality classes. Scaling relations are systematically derived and the known exact [Formula Presented] value is obtained for the voter model universality class. © 1997 The American Physical Society.