Nonequilibrium Phase Transition on a Randomly Diluted Lattice

Vojta, Thomas; Lee, Man Young

doi:10.1103/physrevlett.96.035701

Cited by 56 publications

(77 citation statements)

References 29 publications

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“…For the SIS model, the correction to the scaling provides β/ν ⊥ = 1.403(4), γ/ν ⊥ = 0.209 (2), and ν /ν ⊥ = 1.922 (2), an even better improvement of the estimates as well as their proximities with DP class. In left panel of figure 2, the rescalings by pure power laws, τ /L ν /ν ⊥ and so on, are compared with those given by (8). It is neat the overmatching fit between data and the ansatz (8).…”

Section: Spreading Analysismentioning

confidence: 99%

“…Concomitantly with the increasing interest on absorbing/active phase transitions in complex topologies [3,4,5,6,7], there are still a lot of open problems being intensively investigated on regular lattices such as the effects of quenched disorder [8,9,10], diffusion [11], as well the modeling of predator-prey systems [12], and clonal replication [13,14].…”

Section: Introductionmentioning

confidence: 99%

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Quasi-stationary simulations of the directed percolation universality class ind= 3 dimensions

2009

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Abstract. We present quasi-stationary simulations of three-dimensional models with a single absorbing configuration, viz. the contact process (CP), the susceptibleinfected-susceptible (SIS) and the contact replication process (CRP). The moment ratios of the order parameters for DP class in three dimensions were set up using the well established SIS and CP models. We also show that the mean-field exponents in d = 3 reported previously for CRP [Ferreira SC 2005 Phys. Rev Quasi-stationary simulations of DP class in d = 3 2 IntroductionPhase transitions to a single absorbing configuration, a state in which the system can not scape from, are nowadays a topic in the frontier of Nonequilibrium Statistical Physics [1,2]. Concomitantly with the increasing interest on absorbing/active phase transitions in complex topologies [3,4,5,6,7], there are still a lot of open problems being intensively investigated on regular lattices such as the effects of quenched disorder [8,9,10], diffusion [11], as well the modeling of predator-prey systems [12], and clonal replication [13,14].Under the renormalization group point of view, it is expected [1,15,16] that the absorbing phase transitions in models with a positive one-component order parameter, short-range interactions and without additional symmetries or quenched disorder belong generally to the universality class of directed percolation (DP). This conjecture is known as Janssen-Grassberger criterion [1]. It is worthwhile to mention, the interest on this kind of phase transitions was raised by the recent experimental observation of the DP class in absorbing-state phase transitions [18,19]. On the other hand, while DP is considered the most robust universality class of the absorbing-state phase transitions, the precise numerical determination of the critical exponents of a specific model can be masked by factors like diffusion [11] and weak quenched disorder [10].The contact process (CP), the standard example of the DP universality class, is a toy model of epidemics [20]. ‡. More recently, a novel variation of the CP was introduced for the modeling of clonal (copies of themselves) replication, the contact replication process (CRP) [13,14]. Since neither additional symmetries nor long-range interactions were included, the CRP fulfils the requirements of the Janssen-Gassberger criterion. However, the first dynamic spreading analysis of CRP in d = 1 − 3 dimensions, reported in [13,14] intriguingly classified the model in the DP universality class in one and two, but not in three dimensions. Surprisingly, in d = 3 the reported spreading exponents were those predicted by the mean-field approach [14].In the present work we applied spreading analysis and the method of quasistationary simulations [22,23] in three-dimensional models that fulfill the JanssenGrassberger criterion. Particularly, we turned back to the CRP model and showed that the mean-field behaviour observed previously in d = 3 [14] is a transient associated to the closeness between critical creation and annihilation events. ...

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Section: Spreading Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quasi-stationary simulations of the directed percolation universality class ind= 3 dimensions

2009

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“…Consequently, the contact process on a randomly diluted lattice has two different nonequilibrium transitions (see also Fig. 1), the generic transition for p < p c which is driven by the dynamic fluctuations of the contact process and a percolation transition at p = p c which is driven by the lattice geometry [41]. The two transitions are separated by a multicritical point which was studied in Ref.…”

Section: Model and Phase Transition Scenariosmentioning

confidence: 99%

“…Vojta and Lee [41] developed a theory for this transition by combining the well-known critical behavior of classical percolation with the properties of a supercritical contact process on a finite-size cluster. They found that the behavior of the contact process on a diluted lattice close to the percolation threshold follows the activated scaling scenario of subsection II C. However, the critical exponents differ from those of the generic transition discussed above; they can be expressed as combinations of the classical lattice percolation exponents β c and ν c which are known exactly in two space dimensions.…”

Section: H Spatial Correlationsmentioning

confidence: 99%

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Infinite-randomness critical point in the two-dimensional disordered contact process

2009

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We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte-Carlo simulations for times up to 10 10 and system sizes up to 8000 × 8000 sites. Our data provide strong evidence for the transition being controlled by an exotic infinite-randomness critical point with activated (exponential) dynamical scaling. We calculate the critical exponents of the transition and find them to be universal, i.e., independent of disorder strength. The Griffiths region between the clean and the dirty critical points exhibits power-law dynamical scaling with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder. Our results are of importance beyond absorbing state transitions because according to a strong-disorder renormalization group analysis, our transition belongs to the universality class of the two-dimensional random transverse-field Ising model.

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