Discontinuous transition in a boundary driven contact process

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Abstract

The contact process is a stochastic process which exhibits a continuous, absorbing state phase transition in the directed percolation (DP) universality class. In this work, we consider a contact process with a bias in conjunction with an active wall. This model exhibits waves of activity emanating from the active wall and, when the system is supercritical, propagating indefinitely as travelling (Fisher) waves. In the subcritical phase the activity is localized near the wall. We study the phase transition numerically and show that certain properties of the system, notably the wave velocity, are discontinuous across the transition. Using a modified Fisher equation to model the system we elucidate the mechanism by which the discontinuity arises. Furthermore we establish relations between properties of the travelling wave and DP critical exponents.

Original languageEnglish
Article numberP09008
Pages (from-to)-
Number of pages17
Journal Journal of Statistical Mechanics: Theory and Experiment
DOIs
Publication statusPublished - Sep 2010

Keywords

  • nonequilibrium wetting (theory)
  • phase transitions into absorbing states (theory)
  • stochastic particle dynamics (theory)
  • stationary states
  • BRANCHING RANDOM-WALK
  • DIRECTED PERCOLATION
  • PHASE-TRANSITIONS
  • ABSORBING STATES
  • PROPAGATION
  • SYSTEMS
  • LATTICE

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