Absorbing-state phase transitions with extremal dynamics

Details Absorbing-state phase transitions with extremal dynamics Absorbing-state phase transitions with extremal dynamics

2004-10-11

arxiv.org/abs/cond-mat/0410254v1

Physics

Condensed Matter

Statistical Mechanics

24 pages, 11 figures

Scientific paper

10.1103/PhysRevE.71.066113

Extremal dynamics represents a path to self-organized criticality in which the order parameter is tuned to a value of zero. The order parameter is associated with a phase transition to an absorbing state. Given a process that exhibits a phase transition to an absorbing state, we define an ``extremal absorbing" process, providing the link to the associated extremal (nonabsorbing) process. Stationary properties of the latter correspond to those at the absorbing-state phase transition in the former. Studying the absorbing version of an extremal dynamics model allows to determine certain critical exponents that are not otherwise accessible. In the case of the Bak-Sneppen (BS) model, the absorbing version is closely related to the "$f$-avalanche" introduced by Paczuski, Maslov and Bak [Phys. Rev. E {\bf 53}, 414 (1996)], or, in spreading simulations to the "BS branching process" also studied by these authors. The corresponding nonextremal process belongs to the directed percolation universality class. We revisit the absorbing BS model, obtaining refined estimates for the threshold and critical exponents in one dimension. We also study an extremal version of the usual contact process, using mean-field theory and simulation. The extremal condition slows the spread of activity and modifies the critical behavior radically, defining an ``extremal directed percolation" universality class of absorbing-state phase transitions. Asymmetric updating is a relevant perturbation for this class, even though it is irrelevant for the corresponding nonextremal class.

Affiliated with

Also associated with

No associations

Rating

Absorbing-state phase transitions with extremal dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Absorbing-state phase transitions with extremal dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Absorbing-state phase transitions with extremal dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-714588