Revisiting the one-dimensional diffusive contact process

@article{Dantas2007RevisitingTO,
  title={Revisiting the one-dimensional diffusive contact process},
  author={Wellington G. Dantas and M{\'a}rio J. de Oliveira and J{\"u}rgen F. Stilck},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2007},
  volume={2007},
  pages={P08009 - P08009}
}
In this work we study the one-dimensional contact process with diffusion using two different approaches to estimate the critical properties of this model: the supercritical series expansion and finite size exact solution approaches. We place special emphasis on looking at the multicritical point and its crossover exponent that characterizes the passage between directed percolation and mean-field critical properties. This crossover occurs in the limit of infinite diffusion rate and our results… 
3 Citations
Crossover from directed percolation to mean field behavior in the diffusive contact process
Recently Dantas, Oliveira and Stilck (2007 J. Stat. Mech. P08009) studied how the one-dimensional diffusive contact process crosses over from the critical behavior of directed percolation to an
Quasi-stationary simulations of the directed percolation universality class in d = 3 dimensions
We present quasi-stationary simulations of three-dimensional models with a single absorbing configuration, namely the contact process (CP), the susceptible–infected–susceptible (SIS) model and the
Crossovers from parity conserving to directed percolation universality.
  • G. Ódor, N. Menyhárd
  • Physics
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  • 2008
TLDR
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 and the resulting models show a diversity within the DP universality class in one dimension.

References

SHOWING 1-10 OF 56 REFERENCES
Phase transition in conservative diffusive contact processes.
TLDR
The phase diagrams of conservative diffusive contact processes are determined by means of numerical simulations and indicate that in the limit of infinite diffusion rate the jump in density equals 2/3 for the pair- creation model and 5/6 for the triplet-creation model.
Study of universality crossover in the contact process
We consider a generalization of the contact process stochastic model, including an additional autocatalitic process. The phase diagram of this model in the proper 2-parameter space displays a line of
Time-dependent perturbation theory for nonequilibrium lattice models
We develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. We focus on models such as the contact process which evolve via destruction and autocatalytic creation
Time-dependent perturbation theory for nonequilibrium lattice models.
We develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. We focus on models such as the contact process which evolve via destruction and autocatalytic creation
Rigorous results for the diffusive contact processes in d>or=3
The diffusive contact process is an interacting particle system on the d-dimensional hypercubic lattice. Each site can be occupied by, at most, one particle and each particle can do the following
On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state
It is pointed out that chemical reactions which show an absorbing stationary state in the master-equation approach (e.g. Schlögl's first reaction) exhibit nevertheless a second order phase transition
Density matrix renormalization group and reaction-diffusion processes
Abstract:The density matrix renormalization group ( DMRG) is applied to some one-dimensional reaction-diffusion models in the vicinity of and at their critical point. The stochastic time evolution
First-order phase transition in a one-dimensional nonequilibrium model.
  • Dickman, Tomé
  • Materials Science, Mathematics
    Physical review. A, Atomic, molecular, and optical physics
  • 1991
TLDR
An example of a single-component, one-dimensional interacting particle system with a discontinuous transition into an absorbing state and the basic processes in the model are spontaneous annihilation, autocatalytic creation by trimers, and hopping.
Nonequilibrium Statistical Mechanics in One Dimension: Experimental Results
Part I. Reaction-Diffusion Systems and Models of Catalysis 1. Scaling theories of diffusion-controlled and ballistically-controlled bimolecular reactions S. Redner 2. The coalescence process, A+A->A,
Non-equilibrium critical phenomena and phase transitions into absorbing states
This review addresses recent developments in non-equilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed
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