Survival probability and field theory in systems with absorbing states

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.