Mixed-order phase transition of the contact process near multiple junctions

Abstract

We have studied the phase transition of the contact process near a multiple junction of M semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant (M=2) and semi-infinite (M=1) system, the local order parameter is found to be discontinuous for M>2. Furthermore, the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. In the active phase, the estimate is compatible with the bulk value, while in the inactive phase it exceeds the bulk value and increases with M. The unusual local critical behavior is explained by a scaling theory with an irrelevant variable, which becomes dangerous in the inactive phase. Quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results.

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

“…The local critical behavior of the contact process at multiple junctions has recently been studied and mixedorder transition has been observed [16]. The critical exponents at the junction, such as δ ′ and ν ,1 in the inactive phase are M -dependent, and comparing their values with the series of data in Table II, we can assign an approximate effective parameter A M for each value of M .…”

“…A multiple junction is such a geometry, in which M > 2 semi-infinite chains are connected to a central site [16,[41][42][43]. The local critical behavior of the contact process at multiple junctions has recently been studied and mixedorder transition has been observed [16].…”

“…The observed critical behavior at multiple junctions has been explained within the frame of a scaling theory in Refs. [16,44], which is expected to hold for the problem of the marginal extended defect in the region A > A c . In the following we recapitulate the essential points of this scaling reasoning.…”

“…According to the scaling theory in Ref. [16], when lengths are rescaled by a factor b > 1, so that l → l/b, the survival probability satisfies the relation:…”

“…On the other hand a single defect site represents an irrelevant perturbation, resulting only in correction to scaling terms [15]. Recently, the contact process has been studied near multiple junctions, which are composed of M > 2 semiinfinite one-dimensional lattices connected to a common central site [16]. Near such a junction the model exhibits a mixed-order transition [17]: the local order parameter is discontinuous, at the same time the temporal correlation length diverges algebraically as the critical point is approached.…”