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

TL;DR

This study investigates the critical behavior of the contact process near an extended defect, revealing a rich variety of phase transitions including continuous and mixed-order types, with novel scaling properties in a one-dimensional system.

Contribution

It demonstrates the existence of nonuniversal and anomalous critical behaviors at extended defects in the contact process, including a mixed-order transition with distinct exponents.

Findings

Continuous phase transition with varying critical exponents for weaker defects.

Mixed-order transition with discontinuous order parameter and diverging correlation length.

Scaling theory explains the mixed-order transition regime.

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.