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Generalized contact process with n absorbing states.

J Hooyberghs1, E Carlon, C Vanderzande

  • 1Departement WNI, Limburgs Universitair Centrum, 3590 Diepenbeek, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
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This study explores a one-dimensional lattice model with multiple absorbing states. For n>=3, it conjectures a new universality class with specific critical exponents, linking it to branching annihilating random walks.

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Mathematical Modeling

Background:

  • Investigating critical phenomena in stochastic lattice models is crucial for understanding phase transitions.
  • The behavior of models with multiple absorbing states remains an active area of research.

Purpose of the Study:

  • To analyze the critical properties of a one-dimensional stochastic lattice model with n permutation-symmetric absorbing states.
  • To determine the universality classes and critical exponents for different values of n.

Main Methods:

  • Non-Hermitian density-matrix renormalization group (DMRG) was employed for numerical analysis.
  • Analytical methods were used to map the model dynamics to an n-state Potts model in a specific limit.

Main Results:

Related Experiment Videos

  • For n=1 and n=2, the model belongs to the directed percolation and parity conserving universality classes, respectively.
  • For n=3 and n=4, the model remains in the active phase, with critical points at infinite reaction rates.
  • A conjecture is proposed for n>=3, suggesting a universal behavior with specific critical exponents (z=2, nu_perpendicular=1, beta=1).

Conclusions:

  • The study identifies distinct critical behaviors for small n and proposes a unified universality class for larger n.
  • The findings connect the lattice model to multispecies branching annihilating random walks and the n-state Potts model.
  • Symmetry breaking in the n=3 case leads to transitions into known universality classes (directed percolation or parity conserving).