Interface scaling in the contact process

Abstract

A correspondence between lattice models with absorbing states and models of pinned interfaces in random media can be established by defining local height variables h(x,t) as integrals of the activity at point x up to time t. Within this context we study the interface representation of a prototypical model with absorbing states, the contact process, in dimensions 1-3. Simulations confirm the scaling relation beta(W)=1-straight theta between the interface-width growth exponent beta(W) and the exponent straight theta governing the decay of the order parameter. A scaling property of the height distribution, which serves as the basis for this relation, is also verified. The height-height correlation function shows clear signs of anomalous scaling, in accord with Lopez' analysis [Phys. Rev. Lett. 83, 4594 (1999)], but no evidence of multiscaling.