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

TL;DR

This paper investigates a symmetric sleepy random walkers model within the conserved directed percolation universality class, using exact quasistationary distributions and Monte Carlo simulations to analyze critical properties and exponents.

Contribution

It provides the first analysis of a CDP model with a variable control parameter, combining exact quasistationary distribution calculations with large-scale simulations.

Findings

Critical exponents agree with previous CDP results

Different dynamic exponent z observed in approach to QS regime

Finite-size scaling confirms universality class membership

Abstract

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.