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 P-s(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(-delta). It is not at all obvious how to compute delta in continuous field theories, where P-s(t) is strictly unity for all finite t. We propose here an interpretation for delta 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 delta value is obtained for the voter model universality class.