Universality in Nonequilibrium Lattice Systems

Ódor, Géza

doi:10.1142/6813

Cited by 146 publications

(174 citation statements)

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“…The first one is the probability that there will be at least one active node at time t. This probability is then averaged over the position of the initial active seed. For the contact process, it scales in the same way as the order parameter [12,13] so we have…”

Section: Scaling Theory In An Irfpmentioning

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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Section: Scaling Theory In An Irfpmentioning

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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“…For larger values of ν, however, generic, continuously changing power laws can be observed. In particular for ν = 1.5 simulations We have also performed spreading simulations, starting from a very small initial seed of active sites [9]. These simulations were performed on networks with N = 10 5 nodes up to t = 4 × 10 5 MC time steps.…”

Section: Weighted Ba Trees With Multiplicative Weights: Wbat-i Modelmentioning

confidence: 99%

“…On the other hand, occupied vertices become empty with a unitary rate. On a regular lattice the CP experiences a nonequilibrium phase transition at a critical point λ c , separating an absorbing phase from an active one [8][9][10], whose order parameter is the density of occupied sites ρ in the steady state. Thus, for λ < λ c , an absorbing phase with ρ = 0 is observed, while for λ > λ c the system reaches an active phase, with ρ > 0 in the thermodynamic limit.…”

Section: Introductionmentioning

confidence: 99%

Slow dynamics and rare-region effects in the contact process on weighted tree networks

Ódor

Pastor-Satorras

2012

Phys. Rev. E

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We show that generic, slow dynamics can occur in the contact process on complex networks with a tree-like structure and a superimposed weight pattern, in the absence of additional (nontopological) sources of quenched disorder. The slow dynamics is induced by rare-region effects occurring on correlated subspaces of vertices connected by large weight edges and manifests in the form of a smeared phase transition. We conjecture that more sophisticated network motifs could be able to induce Griffiths phases, as a consequence of purely topological disorder.

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“…The research of nonequilibrium models has been a central topic of statistical mechanics [1][2][3]. A fundamental dynamical model to understand them is the contact process (CP) [4,5], in which sites can be either active (infected) or inactive (susceptible).…”

Section: Introductionmentioning

confidence: 99%

Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks

Ódor

2013

Phys. Rev. E

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I extend a previous work to susceptible-infected-susceptible (SIS) models on weighted Barabási-Albert scale-free networks. Numerical evidence is provided that phases with slow, power-law dynamics emerge as the consequence of quenched disorder and tree topologies studied previously with the contact process. I compare simulation results with spectral analysis of the networks and show that the quenched mean-field (QMF) approximation provides a reliable, relatively fast method to explore activity clustering. This suggests that QMF can be used for describing rare-region effects due to network inhomogeneities. Finite-size study of the QMF shows the expected disappearance of the epidemic threshold λ c in the thermodynamic limit and an inverse participation ratio ∼0.25, meaning localization in case of disassortative weight scheme. Contrarily, for the multiplicative weights and the unweighted trees, this value vanishes in the thermodynamic limit, suggesting only weak rare-region effects in agreement with the dynamical simulations. Strong corrections to the mean-field behavior in case of disassortative weights explains the concave shape of the order parameter ρ(λ) at the transition point. Application of this method to other models may reveal interesting rare-region effects, Griffiths phases as the consequence of quenched topological heterogeneities.

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Universality in Nonequilibrium Lattice Systems

Cited by 146 publications

References 0 publications

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

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

Slow dynamics and rare-region effects in the contact process on weighted tree networks

Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks

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