Static critical behavior in the inactive phase of the pair contact process.

Abstract

Steady-state properties in the absorbing phase of the 1d pair contact process model are investigated. It is shown that, in typical absorbing states (reached by the system's dynamic rules), the density of isolated particles rho(1), approaches a stationary value that depends on the annihilation probability (p); the deviation from its "natural" value at criticality rho(nat)(1) follows a power law: rho(nat)(1)-rho(1) approximately (p-p(c))(beta(1)) for p>p(c). Monte Carlo simulations yield beta(1)=0.81. A cluster approximation is developed for this model, qualitatively confirming the numerical results and predicting beta(1)=1. The singular behavior of the isolated particles density in the inactive phase is explained using a phenomenological approach.