We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of λ(l)-λ(∞)=Al-s, with l being the distance from the surface. We concentrate on the marginal situation s=1/ν, where ν 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<Ac, the phase transition is continuous, having an order-parameter critical exponent, which varies continuously with A. For stronger local activation rates A>Ac, 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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics