Nonequilibrium phase transition in a spreading process on a timeline

TL;DR

This paper studies a nonequilibrium process on a timeline with non-Markovian updates, revealing a phase transition driven by temporal Levy flights, analyzed through simulations and field theory.

Contribution

It introduces a model of a non-Markovian spreading process with algebraic waiting times and characterizes its phase transition using numerical and theoretical methods.

Findings

Identifies a nonequilibrium phase transition driven by temporal Levy flights.

Provides numerical estimates of critical exponents.

Shows agreement between simulations and field-theoretic predictions.

Abstract

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 flights in the limit of zero space dimensions. The critical properties are investigated by extensive numerical simulations and compared with field-theoretic predictions.