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

Dantas, W. G.; Oliveira, Mário J. de; Stilck, Jürgen F.

doi:10.1590/s0103-97332008000100018

Cited by 3 publications

(2 citation statements)

References 13 publications

(16 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present paper we extend the results obtained in a preliminary work [9], where we intented to obtain the behavior of this crossover exponent for larger values of the diffusion rate using a numerical simulational approach to determine the critical line as a function of this rate. This numerical simulational approach follows the algorithm proposed by Grassberger and De La Torre [10] to explore the time evolution of the system from an initial condition where a unique seed is present in the system.…”

Section: Introductionmentioning

confidence: 55%

Simulational study for the crossover in the generalized contact process with diffusion

Dantas,

de Oliveira,

Stilck

2008

Preprint

Self Cite

View full text Add to dashboard Cite

In a recent work, Dantas and Stilck studied a model that generalizes the contact process model with diffusion [1]. Our approach, based on the supercritical expansion, showed that for a weak diffusion regime the crossover exponent between the directed percolation and compact directed percolation universality classes was φ ≈ 2. However this approach did not work for reduced diffusion rates higher than D ≈ 0.3, where 0 ≤ D ≤ 1 and D = 1 corresponds to an infinite diffusion rate. Thus, in the present work we estimate this crossover exponent for higher diffusion rates using a numerical simulation approach.

show abstract

Section: Introductionmentioning

confidence: 55%

Simulational study for the crossover in the generalized contact process with diffusion

Dantas,

de Oliveira,

Stilck

2008

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…has been determined in case of DP to the compact DP class [34,35,36,37]. Crossover between DP and isotropic percolation was investigated by field theory [38,39,40] and simulations [41].…”

Section: Introductionmentioning

confidence: 99%

Crossovers from parity conserving to directed percolation universality

Odor,

Menyhard

2008

Preprint

View full text Add to dashboard Cite

The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z2 symmetric absorbing phases (the NEKIMCA and Grassberger's A stochastic cellular automaton) the introduction of an external symmetry breaking field causes a crossover to kink parity conserving models characterized by dynamical scaling of the directed percolation (DP) and the crossover exponent: 1/φ ≃ 0.53(2). In case an even offspringed branching and annihilating random walk model (dual to NEKIMCA) the introduction of spontaneous particle decay destroys the parity conservation and results in a crossover to the DP class characterized by the crossover exponent: 1/φ ≃ 0.205(5). The two different kinds of crossover operators can't be mapped onto each other and the resulting models show a diversity within the DP universality class in one dimension. These 'sub-classes' differ in cluster scaling exponents.

show abstract

Crossovers from parity conserving to directed percolation universality

Ódor

Menyhárd

2008

Phys. Rev. E

View full text Add to dashboard Cite

The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z_2 symmetric absorbing phases (the cellular automaton version of the nonequilibrium kinetic Ising model (NEKIMCA) and a stochastic cellular automaton invented by Grassberger, Krause, and von der Twer [J. Phys. A 17, L105 (1984)]) the introduction of an external symmetry breaking field causes a crossover to kink parity conserving models characterized by dynamical scaling of the directed percolation (DP) and the crossover exponent: 1/phi approximately equal to 0.53(2) . In the case of a branching and annihilating random walk model with an even number of offspring (dual to NEKIMCA) the introduction of spontaneous particle decay destroys the parity conservation and results in a crossover to the DP class characterized by the crossover exponent: 1/phi approximately equal to 0.205(5) . The two different kinds of crossover operators cannot be mapped onto each other and the resulting models show a diversity within the DP universality class in one dimension. These subclasses differ in cluster scaling exponents.

show abstract

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

Cited by 3 publications

References 13 publications

Simulational study for the crossover in the generalized contact process with diffusion

Simulational study for the crossover in the generalized contact process with diffusion

Crossovers from parity conserving to directed percolation universality

Crossovers from parity conserving to directed percolation universality

Contact Info

Product

Resources

About