Multicritical behaviour of the diluted contact process

Dahmen, Sílvio R.; Sittler, Lionel; Hinrichsen, Haye

doi:10.1088/1742-5468/2007/01/p01011

Cited by 16 publications

(18 citation statements)

References 24 publications

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“…This critical behavior places the quenched diluted contact process into the universality class of the random transverse-field Ising model [14,15,16,17,18,19,20,21]. The slow activated dynamics of the quenched diluted contact process has been confirmed by numerical simulations in two dimensions [8,9,10,11].…”

Section: Introductionmentioning

confidence: 73%

“…A straightforward numerical approach to the diluted contact process is to consider all the remaining sites of a lattice after a certain fraction of them has been removed [6,7,10]. Other methods such as ours consider instead just the sites of the percolating cluster [9,11]. In this case the total computer time should include the time it takes to generate the percolating cluster.…”

Section: Introductionmentioning

confidence: 99%

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Critical properties of the contact process with quenched dilution

Wada¹,

Oliveira²

2017

J. Stat. Mech.

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Abstract.We have studied the critical properties of the contact process on a square lattice with quenched site dilution by Monte Carlo simulations. This was achieved by generating in advance the percolating cluster, through the use of an appropriate epidemic model, and then by the simulation of the contact process on the top of the percolating cluster. The dynamic critical exponents were calculated by assuming an activated scaling relation and the static exponents by the usual power law behavior. Our results are in agreement with the prediction that the quenched diluted contact process belongs to the universality class of the random transverse-field Ising model. We have also analyzed the model and determined the phase diagram by the use of a mean-field theory that takes into account the correlation between neighboring sites.

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Section: Introductionmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Critical properties of the contact process with quenched dilution

Wada¹,

Oliveira²

2017

J. Stat. Mech.

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“…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%

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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“…The contact process with quenched spatial disorder shows infinite-disorder criticality [18][19][20], while for temporal disorder, following early numerical works [21,22], a so called infinite-noise critical behavior was found by a real-time renormalization group method [23]. This model has also been studied with long-range interactions [24,25], on fractals [26] and different kinds of * Electronic address: juhasz.robert@wigner.mta.hu † Electronic address: igloi.ferenc@wigner.mta.hu complex networks [27,28]. We also mention that, in a one-dimensional model of diffusing particles, a single boundary site evolving according to the dynamics of the contact process is able to induce an absorbing phase transition [29].…”

Section: Introductionmentioning

confidence: 94%

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

Juhász

Iglói

2018

Phys. Rev. E

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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 , 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.

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Multicritical behaviour of the diluted contact process

Cited by 16 publications

References 24 publications

Critical properties of the contact process with quenched dilution

Critical properties of the contact process with quenched dilution

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

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

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