Non-equilibrium phase transition in a spreading process on a timeline

Andre C Barato, Haye Hinrichsen
2009 Journal of Statistical Mechanics: Theory and Experiment  
We consider a nonequilibrium process on a timeline with discrete sites which evolves by a non-Markovian update rule in such a way that an active site at time t activates one or several sites in the future at time t+dt. The time intervals dt are distributed algebraically as dt^(-1-kappa), where 0<kappa<1 is a control paramter. Depending on the activation rate, the system display a nonequilibrium phase transition which may be interpreted as directed percolation transition driven by temporal Levy
more » ... lights in the limit of zero space dimensions. The critical properties are investigated by extensive numerical simulations and compared with field-theoretic predictions.
doi:10.1088/1742-5468/2009/02/p02020 fatcat:hjirew3i3nhgdp5mc632veemoy