Study of universality crossover in the contact process

Dantas, W. G.; Stilck, Jürgen F.

doi:10.1088/0305-4470/38/26/001

Cited by 9 publications

(28 citation statements)

References 25 publications

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“…Our result, φ = 4.02 ± 0.13 is in agreement with that derived in [10] and explores a region of diffusion very close to the multicritical point. The technique of the two-variable supercritical series associated with PDA analysis was shown to be accurate enough to determine the critical properties in similar models [11,20]. Therefore, we believe that a natural extension for this work is analyze related models that apparently possess non-trivial multicritical points.…”

Section: Resultsmentioning

confidence: 93%

“…Note that as the value of D =D/(1 +D) grows the dispersion in the value estimates also grows. neighborhood of a multicritical point the reduction of a two-variable series to one variable leads to very poor estimates of the critical properties [11] close to a multicritical point.…”

Section: Analysis Of the Seriesmentioning

confidence: 99%

“…In the present work, we obtain estimates for the critical line and the crossover exponent φ using a two-variable supercritical series analyzed using partial differential approximants (PDAs) [15,17,18]. This technique seems to be more appropriate for the analysis of a two-variable series with a multicritical behavior, as shown by the results obtained from other models [11,19]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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A supercritical series analysis for the generalized contact process with diffusion

Dantas¹,

Stilck²

2007

J. Stat. Mech.

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We study a model that generalizes the CP with diffusion. An additional transition is included in the model so that at a particular point of its phase diagram a crossover from the directed percolation to the compact directed percolation class will happen. We are particularly interested in the effect of diffusion on the properties of the crossover between the universality classes. To address this point, we develop a supercritical series expansion for the ultimate survival probability and analyse this series using d-log Padé and partial differential approximants. We also obtain approximate solutions in the one-and two-site dynamical mean-field approximations. We find evidences that, at variance to what happens in mean-field approximations, the crossover exponent remains close to φ = 2 even for quite high diffusion rates, and therefore the critical line in the neighborhood of the multicritical point apparently does not reproduce the mean-field result (which leads to φ = 0) as the diffusion rate grows without bound.

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Section: Resultsmentioning

confidence: 93%

Section: Analysis Of the Seriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A supercritical series analysis for the generalized contact process with diffusion

Dantas¹,

Stilck²

2007

J. Stat. Mech.

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“…In a recent paper, we estimated the crossover exponent between the DP and DCP classes [9]. Using the perturbative supercritical series expansion formalism, proposed by Dickman and Jensen [5], we obtain a very precise estimates for this exponent in a generalized contact process (CP) model, * Electronic address: wgd@gibbs.if.usp.br † Electronic address: oliveira@if.usp.br ‡ Electronic address: jstilck@if.uff.br which lead us to conjecture that φ = 2, in accordance with upper bound estimates [10] and simulational results for the Domany-Kinzel cellular automaton [11], which may indicate that this exponent is the same for similar models with paralell and sequencial updates.…”

Section: Introductionmentioning

confidence: 99%

Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

Dantas

Oliveira

Stilck³

2008

Braz. J. Phys.

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We study how the crossover exponent, φ, between the directed percolation (DP) and compact directed percolation (CDP) behaves as a function of the diffusion rate in a model that generalizes the contact process. Our conclusions are based in results pointed by perturbative series expansions and numerical simulations, and are consistent with a value φ = 2 for finite diffusion rates and φ = 1 in the limit of infinite diffusion rate.

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“…A different approach based on partial differential approximants (PDA's) has been used by Dantas and Stilck in Ref. [17], who applied the supercritical series expansion to study the crossover between the 1d CP and the voter model [6], thereby introducing a second control parameter to the perturbation theory. We also use PDA's in order to compare results from the two extrapolation methods.…”

Section: Introductionmentioning

confidence: 99%

Supercritical series expansion for the contact process in heterogeneous and disordered environments

Neugebauer

Taraskin²

2007

Phys. Rev. E

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The supercritical series expansion of the survival probability for the one-dimensional contact process in heterogeneous and disordered lattices is used for the evaluation of the loci of critical points and critical exponents beta . The heterogeneity and disorder are modeled by considering binary regular and irregular lattices of nodes characterized by different recovery rates and identical transmission rates. Two analytical approaches based on nested Padé approximants and partial differential approximants were used in the case of expansions with respect to two variables (two recovery rates) for the evaluation of the critical values and critical exponents. The critical exponents in heterogeneous systems are very close to those for the homogeneous contact process thus confirming that the contact process in periodic heterogeneous environment belongs to the directed percolation universality class. The disordered systems, in contrast, seem to have continuously varying critical exponents.

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Study of universality crossover in the contact process

Cited by 9 publications

References 25 publications

A supercritical series analysis for the generalized contact process with diffusion

A supercritical series analysis for the generalized contact process with diffusion

Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

Supercritical series expansion for the contact process in heterogeneous and disordered environments

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