Survival probability and field theory in systems with absorbing states

An important quantity in the analysis of systems with absorbing states is the survival probability Pₛ(t), the probability that an initial localized seed of particles has not completely disappeared after time t. At the transition into the absorbing phase, this probability scales for large t like t^-δ. It is not at all obvious how to compute δ in continuous field theories, where Pₛ(t) is strictly unity for all finite t. We propose here an interpretation for δ 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 δ value is obtained for the voter model universality class.