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Mean-field theory for the long-range contact process with diffusion.

T B Pedro1, W Figueiredo1, A L Ferreira2

  • 1Departamento de Física, Universidade Federal de Santa Catarina, Florianópolis, 88040-900 Santa Catarina, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2015
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Summary
This summary is machine-generated.

Diffusion impacts phase transitions in one-dimensional long-range contact processes. Higher diffusion requires stronger interactions for phase coexistence, with system size crucial for accurate correlation analysis.

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Long-range contact processes exhibit phase transitions influenced by diffusion.
  • Previous studies indicate diffusion weakens long-range interactions, altering transition characteristics.

Purpose of the Study:

  • Investigate the effect of diffusion on the one-dimensional long-range contact process.
  • Determine the influence of system size (L) on phase transition behavior under varying diffusion rates.

Main Methods:

  • Utilized a generalized mean-field approximation for the master equation.
  • Analyzed systems with aggregates of L lattice sites, up to L=10.
  • Performed extrapolations to infinite-sized systems for specific diffusion rates.

Main Results:

  • Obtained the phase diagram for L up to 10.
  • Confirmed that diffusion suppresses phase coexistence, especially in high-diffusion regimes.
  • Demonstrated the necessity of larger L values for accurately capturing correlations in high-diffusion scenarios.

Conclusions:

  • The study provides insights into diffusion's role in phase transitions of long-range contact processes.
  • A generalized mean-field approach with sufficient system size (L) is effective.
  • An efficient method for studying mean-field equations and determining phase transition nature is presented.