Critical properties of the contact process with quenched dilution

Wada, Alexander H. O.; Oliveira, Mário J. de

doi:10.1088/1742-5468/aa694b

Cited by 9 publications

(9 citation statements)

References 27 publications

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“…From the data shown in the inset of Fig. 7, we find δ = 2.1(3), very close to the value δ = 1.9(2) observed for the usual CP with random dilution, indicating that critical behavior of the disordered model belongs to the universality class of the diluted CP [24,30].…”

Section: B Symmetric Disordersupporting

confidence: 76%

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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Section: B Symmetric Disordersupporting

confidence: 76%

Quenched disorder in the contact process on bipartite sublattices

2019

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“…Here we consider just the second approach, applying it to the SIS model. It is worth mentioning that the stationary properties of the SIS model with the first approach to vaccination are identified with contact process under quenched dilution [35][36][37][38].…”

Section: Vaccination Processmentioning

confidence: 99%

Effect of immunization through vaccination on the SIS epidemic spreading model

Tomé,

de Oliveira

2021

Preprint

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We analyze the susceptible-infected-susceptible model for epidemic spreading in which a fraction of the individuals become immune by vaccination. This process is understood as a dilution by vaccination, which decreases the fraction of the susceptible individuals. For a nonzero fraction of vaccinated individuals, the model predicts a new state in which the disease spreads but eventually becomes extinct. The new state emerges when the fraction of vaccinated individuals is greater than a critical value. The model predicts that this critical value increases as one increases the infection rate reaching an asymptotic value, which is strictly less than the unity. Above this asymptotic value, the extinction occurs no matter how large the infection rate is.

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“…The first major result on disorder relevance was brought forward by Harris in 1974 [21], who argued that disorder is relevant when < 2, where is the dimension of the system and denotes the correlation length exponent. Using Harris' criterion, numerical results on 2D diluted regular lattices can be entirely explained, including the rise of non-conventional activated scaling and strong Griffiths effects for the contact process (CP) [22][23][24], as well as ambiguities related to strong logarithmic corrections for the Ising model [25][26][27][28][29][30][31][32][33], which represents the marginal case, as in two dimensions = 1. Despite its success in describing the effects of uncorrelated disorder, the Harris criterion fails to explain certain results for the Ising model and CP on two-dimensional Delaunay triangulations [34][35][36][37][38][39], where both systems retain their clean universal properties.…”

Section: Introductionmentioning

confidence: 99%

Universality of continuous phase transitions on random Voronoi graphs

Schrauth¹,

Portela²

2019

Phys. Rev. E

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The Voronoi construction is ubiquitous across the natural sciences and engineering. In statistical mechanics, though, critical phenomena have so far been only investigated on the Delaunay triangulation, the dual of a Voronoi graph. In this paper we set to fill this gap by studying the two most prominent systems of classical statistical mechanics, the equilibrium spin-1/2 Ising model and the non-equilibrium contact process, on two-dimensional random Voronoi graphs. Particular motivation comes from the fact that these graphs have vertices of constant coordination number, making it possible to isolate topological effects of quenched disorder from node-intrinsic coordination number disorder. Using large-scale numerical simulations and finite-size-scaling techniques, we are able to demonstrate that both systems belong to their respective clean universality classes. Therefore, quenched disorder introduced by the randomness of the lattice is irrelevant and does not influence the character of the phase transitions. We report the critical points of both models to considerable precision and, for the Ising model, also the first correction-to-scaling exponent.

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Critical properties of the contact process with quenched dilution

Cited by 9 publications

References 27 publications

Quenched disorder in the contact process on bipartite sublattices

Quenched disorder in the contact process on bipartite sublattices

Effect of immunization through vaccination on the SIS epidemic spreading model

Universality of continuous phase transitions on random Voronoi graphs

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