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Conserved contact process in one to five dimensions.

Munir M S Sabag1, Mário J De Oliveira

  • 1Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 9, 2002
PubMed
Summary

This study investigates the conserved contact process in hypercubic lattices. Numerical simulations reveal critical points and fractal dimensions, with exact stationary states found for two particles.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Lattice Models

Background:

  • The ordinary contact process is a fundamental model for diffusion and reaction dynamics.
  • Conserved particle number introduces unique constraints, altering system behavior.
  • Understanding lattice-based models is crucial for various scientific fields.

Purpose of the Study:

  • To analyze the conserved contact process in hypercubic lattices (1D to 5D).
  • To determine critical parameters like critical point, critical exponent beta, and fractal dimension d(F).
  • To investigate the exact stationary state for a two-particle system.

Main Methods:

  • Numerical simulations were employed to study the process.
  • Analysis focused on hypercubic lattices across dimensions one to five.
  • Exact solutions were derived for the specific case of two particles.

Main Results:

  • The critical point was identified for the conserved contact process.
  • The critical exponent beta and fractal dimension d(F) were determined.
  • An exact stationary state was found for the two-particle system in all dimensions.

Conclusions:

  • The conserved contact process exhibits distinct critical behavior compared to the ordinary contact process.
  • Lattice dimensionality significantly influences the system's critical properties.
  • The two-particle case provides a solvable benchmark for conserved particle systems.

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