| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Fed Minas Gerais, BR-30161970 Belo Horizonte, MG - Brazil
[2] Ecole Normale Super, F-75005 Paris - France
[3] Ctr Wiskunde & Informat, NL-1098 XG Amsterdam - Netherlands
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Journal of Statistical Physics; v. 138, n. 1-3, p. 126-142, FEB 2010. |
| Web of Science Citations: | 25 |
| Abstract | |
We study a particle system with hopping (random walk) dynamics on the integer lattice a{''}currency sign (d) . The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of particles; there is no limit on the number of particles at a given site. Isolated active particles fall asleep at rate lambda > 0, and then remain asleep until joined by another particle at the same site. The state in which all particles are inactive is absorbing. Whether activity continues at long times depends on the relation between the particle density zeta and the sleeping rate lambda. We discuss the general case, and then, for the one-dimensional totally asymmetric case, study the phase transition between an active phase (for sufficiently large particle densities and/or small lambda) and an absorbing one. We also present arguments regarding the asymptotic mean hopping velocity in the active phase, the rate of fixation in the absorbing phase, and survival of the infinite system at criticality. Using mean-field theory and Monte Carlo simulation, we locate the phase boundary. The phase transition appears to be continuous in both the symmetric and asymmetric versions of the process, but the critical behavior is very different. The former case is characterized by simple integer or rational values for critical exponents (beta=1, for example), and the phase diagram is in accord with the prediction of mean-field theory. We present evidence that the symmetric version belongs to the universality class of conserved stochastic sandpiles, also known as conserved directed percolation. Simulations also reveal an interesting transient phenomenon of damped oscillations in the activity density. (AU) | |