Monte Carlo simulations of the clean and disordered contact process in three dimensions

Vojta, Thomas

doi:10.1103/physreve.86.051137

Cited by 39 publications

(41 citation statements)

References 57 publications

(137 reference statements)

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“…The straight lines on the logarithmic plot of δ eff at λ 1 suggest ultraslow dynamics as in the case of a strong disorder fixed point [10]. Indeed, a logarithmic fitting at λ = 0.88 results in P (t) ln(t) −3.5(3) , which is rather close to the the three-dimensional strong disorder universal behavior [40,41]. Simulations started from fully active sites show analogous decay curves for the density of active sites ρ(t), expressing a rapidity reversal symmetry, characteristic of the directed percolation (DP) universality class [36], governing the critical behavior of such models [42].…”

Section: B Variable Threshold Modelmentioning

confidence: 61%

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Critical dynamics on a large human Open Connectome network

Ódor

2016

Phys. Rev. E

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Extended numerical simulations of threshold models have been performed on a human brain network with N = 836 733 connected nodes available from the Open Connectome Project. While in the case of simple threshold models a sharp discontinuous phase transition without any critical dynamics arises, variable threshold models exhibit extended power-law scaling regions. This is attributed to fact that Griffiths effects, stemming from the topological or interaction heterogeneity of the network, can become relevant if the input sensitivity of nodes is equalized. I have studied the effects of link directness, as well as the consequence of inhibitory connections. Nonuniversal power-law avalanche size and time distributions have been found with exponents agreeing with the values obtained in electrode experiments of the human brain. The dynamical critical region occurs in an extended control parameter space without the assumption of self-organized criticality.

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Section: B Variable Threshold Modelmentioning

confidence: 61%

“…In the case of various quenched heterogeneities, a similar model, the CP, has recently been studied on three-dimensional lattices with diluted disorder in [40]. Extensive computer simulations gave numerical evidence for nonuniversal power laws typical of a Griffiths phase as well as activated scaling at criticality.…”

Section: Dynamical Simulation Resultsmentioning

confidence: 99%

Critical dynamics on a large human Open Connectome network

Ódor

2016

Phys. Rev. E

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“…Note that deviations between the SDRG and Monte Carlo estimates have been established also in the case of the contact process on hypercubic lattices with parameter disorder [46]. be needed, or, possibly, other forms of disorder, where the finite-size corrections have a different sign.…”

Section: Discussionmentioning

confidence: 99%

Infinite randomness critical behavior of the contact process on networks with long-range connections

Juhász¹,

Kovács²

2013

J. Stat. Mech.

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Abstract. The contact process and the slightly different susceptible-infectedsusceptible model are studied on long-range connected networks in the presence of random transition rates by means of a strong disorder renormalization group method and Monte Carlo simulations. We focus on the case where the connection probability decays with the distance l as p(l) ≃ βl −2 in one dimension. Here, the graph dimension of the network can be continuously tuned with β. The critical behavior of the models is found to be described by an infinite randomness fixed point which manifests itself in logarithmic dynamical scaling. Estimates of the complete set of the critical exponents, which are found to vary with the graph dimension, are provided by different methods. According to the results, the additional disorder of transition rates does not alter the infinite randomness critical behavior induced by the disordered topology of the underlying random network. This finding opens up the possibility of the application of an alternative tool, the strong disorder renormalization group method to dynamical processes on topologically disordered structures. As the random transverse-field Ising model falls into the same universality class as the random contact process, the results can be directly transferred to that model defined on the same networks.

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“…Hooyberghs et al [24] im-plemented a strong-disorder renormalization group (RG) [25,26] for the disordered contact process and predicted that the transition is controlled by an exotic infiniterandomness critical point (at least for sufficiently strong disorder [27]), accompanied by strong power-law Griffiths singularities [28,29]. The infinite-randomness critical point was confirmed by extensive Monte-Carlo simulations in one, two and three space dimensions [30][31][32][33]. Analogous behavior was found in diluted systems close to the percolation threshold [34] and in quasiperiodic systems [35] (for a review, see Ref.…”

Section: Introductionmentioning

confidence: 99%

Contact process with temporal disorder

2016

Self Cite

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We investigate the influence of time-varying environmental noise, i.e., temporal disorder, on the nonequilibrium phase transition of the contact process. Combining a real-time renormalization group, scaling theory, and large scale Monte-Carlo simulations in one and two dimensions, we show that the temporal disorder gives rise to an exotic critical point. At criticality, the effective noise amplitude diverges with increasing time scale, and the probability distribution of the density becomes infinitely broad, even on a logarithmic scale. Moreover, the average density and survival probability decay only logarithmically with time. This infinite-noise critical behavior can be understood as the temporal counterpart of infinite-randomness critical behavior in spatially disordered systems, but with exchanged roles of space and time. We also analyze the generality of our results, and we discuss potential experiments.

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Monte Carlo simulations of the clean and disordered contact process in three dimensions

Cited by 39 publications

References 57 publications

Critical dynamics on a large human Open Connectome network

Critical dynamics on a large human Open Connectome network

Infinite randomness critical behavior of the contact process on networks with long-range connections

Contact process with temporal disorder

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