Conserved directed percolation: exact quasistationary distribution of small systems and Monte Carlo simulations

Julio Cesar Mansur Filho, Ronald Dickman

Published 2011-03-14Version 1

We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phase transition in the conserved directed percolation (CDP) universality class. Unlike most examples of this class studied previously, this model possesses a continuously variable control parameter, facilitating analysis of critical properties. We study the model using two complementary approaches: analysis of the numerically exact quasistationary (QS) probability distribution on rings of up to 22 sites, and Monte Carlo simulation of systems of up to 32000 sites. The resulting estimates for critical exponents beta, beta/nu_perp, and z, and the moment ratio m_{211} = < rho^2 >/< rho >^2 (rho is the activity density), based on finite-size scaling at the critical point, are in agreement with previous results for the CDP universality class. We find, however, that the approach to the QS regime is characterized by a different value of the dynamic exponent z than found in the QS regime.