Critical Dynamics of the Contact Process with Quenched Disorder

Abstract

We study critical spreading dynamics in the two-dimensional contact process (CP) with quenched disorder in the form of random dilution. In the pure model, spreading from a single particle at the critical point ${\lambda }_c$ is characterized by the critical exponents of directed percolation: in $2+1$ dimensions, $\delta =0.46$, $\eta =0.214$, and $z=1.13$. Disorder causes a dramatic change in the critical exponents, to $\delta \simeq 0.60$, $\eta \simeq -0.42$, and $z\simeq 0.24$. These exponents govern spreading following a long crossover period. The usual hyperscaling relation, $4\delta +2\eta =dz$, is violated. Our results support the conjecture by Bramson, Durrett, and Schonmann [Ann. Prob. {\bf 19}, 960 (1991)], that in two or more dimensions the disordered CP has only a single phase transition.

11 pages, REVTeX, four figures available on request