Critical behavior of a contact process with aperiodic transition rates

Faria, Maicon S.; Ribeiro, Darielder Jesus; Salinas, S. R.

doi:10.1088/1742-5468/2008/01/p01022

Cited by 9 publications

(11 citation statements)

References 36 publications

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“…Quenched disorder, in the form of impurities and defects, plays an important role in real systems, and may be responsible for the rarity of experimental realizations of DP [14]. Quenched disorder in the contact process on a regular lattice has been studied in the forms of random deletion of sites or bonds [15,16,17], and of random spatial variation of the control parameter [18,19,20]. All these studies report a change in the critical behavior of the model.…”

Section: Introductionmentioning

confidence: 99%

Contact process on a Voronoi triangulation

et al. 2008

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We study the continuous absorbing-state phase transition in the contact process on the VoronoiDelaunay lattice. The Voronoi construction is a natural way to introduce quenched coordination disorder in lattice models. We simulate the disordered system using the quasistationary simulation method and determine its critical exponents and moment ratios. Our results suggest that the critical behavior of the disordered system is unchanged with respect to that on a regular lattice, i.e., that of directed percolation.

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Section: Introductionmentioning

confidence: 99%

Contact process on a Voronoi triangulation

et al. 2008

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“…The steps in the observables can be determined from Eqs (36). to(38) yielding ln(ρ) = ln(P s ) = 0.2819, ln(N s ) = 1.104, and ln[ln(t/t 0 )] = 0.5290. k 4.…”

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confidence: 99%

Contact process on generalized Fibonacci chains: Infinite-modulation criticality and double-log periodic oscillations

2014

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We study the nonequilibrium phase transition of the contact process with aperiodic transition rates using a real-space renormalization group as well as Monte Carlo simulations. The transition rates are modulated according to the generalized Fibonacci sequences defined by the inflation rules A → ABk and B → A. For k=1 and 2, the aperiodic fluctuations are irrelevant, and the nonequilibrium transition is in the clean directed percolation universality class. For k≥3, the aperiodic fluctuations are relevant. We develop a complete theory of the resulting unconventional "infinite-modulation" critical point, which is characterized by activated dynamical scaling. Moreover, observables such as the survival probability and the size of the active cloud display pronounced double-log periodic oscillations in time which reflect the discrete scale invariance of the aperiodic chains. We illustrate our theory by extensive numerical results, and we discuss relations to phase transitions in other quasiperiodic systems.

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“…The inclusion of disorder can affect the critical behavior of nonequilibrium phase transitions dramatically. In real systems, quenched disorder is observed in the form of impurities and defects [16], whereas in a regular lattice it can be included in the forms of random deletion of sites or bonds [17][18][19] or random spatial variation of the control parameter [20,21]. According to the Harris' criterion [22], quenched disorder is a relevant perturbation, from the field-theoretical point of view, if dν ⊥ < 2, where d is the dimensionality and ν ⊥ is the correlation length exponent of the pure model.…”

Section: Introductionmentioning

confidence: 99%

Quenched disorder in the contact process on bipartite sublattices

2019

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We study the effects of distinct types of quenched disorder in the contact process (CP) with a competitive dynamics on bipartite sublattices. In the model, the particle creation depends on its first and second neighbors and the extinction increases according to the local density. The clean (without disorder) model exhibits three phases: inactive (absorbing), active symmetric and active asymmetric, where the latter exhibits distinct sublattice densities. These phases are separated by continuous transitions; the phase diagram is reentrant. By performing mean field analysis and Monte Carlo simulations we show that symmetric disorder destroys the sublattice ordering and therefore the active asymmetric phase is not present. On the other hand, for asymmetric disorder (each sublattice presenting a distinct dilution rate) the phase transition occurs between the absorbing and the active asymmetric phases. The universality class of this transition is governed by the less disordered sublattice.

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Critical behavior of a contact process with aperiodic transition rates

Cited by 9 publications

References 36 publications

Contact process on a Voronoi triangulation

Contact process on a Voronoi triangulation

Contact process on generalized Fibonacci chains: Infinite-modulation criticality and double-log periodic oscillations

Quenched disorder in the contact process on bipartite sublattices

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