Nonuniversal and anomalous critical behavior of the contact process near an extended defect

Abstract

We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of $\lambda (l)-\lambda (\infty )=A{l}^{-s}$, $l$ being the distance from the surface. We concentrate on the marginal situation, $s=1/{\nu }_{\perp }$, where ${\nu }_{\perp }$ is the critical exponent of the spatial correlation length, and study the local critical properties of the one-dimensional model by Monte Carlo simulations. The system exhibits a rich surface critical behavior. For weaker local activation rates, $A<A_c$, the phase transition is continuous, having an order-parameter critical exponent, which varies continuously with $A$. For stronger local activation rates, $A>A_c$, the phase transition is of mixed order: the surface order parameter is discontinuous, at the same time the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. The mixed-order transition regime is analogous to that observed recently at a multiple junction and can be explained by the same type of scaling theory.

8 pages, 8 figures

References in corpus (7)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Griffiths phases on complex networks
• Mixed-order phase transition of the contact process near multiple junctions
• Multicritical behavior of the diluted contact process
• Boundary-induced nonequilibrium phase transition into an absorbing state
• Critical phenomena on k-booklets
• Directed percolation with a single defect site

Cited by in corpus (1)

• Heterogeneous excitable systems exhibit Griffiths phases below hybrid phase transitions