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Dynamic phase transition in the contact process with spatial disorder: Griffiths phase and complex persistence

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This study introduces a model exhibiting the Griffiths phase with continuously varying exponents. It shows complex exponents in the active phase, leading to logarithmic periodic oscillations in persistence.

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Area of Science:

  • Statistical Physics
  • Complex Systems Modeling

Background:

  • The Griffiths phase is characterized by algebraic decay with continuously varying exponents.
  • Understanding phase transitions and critical phenomena is crucial in statistical physics.

Purpose of the Study:

  • To present a novel one-dimensional model exhibiting the Griffiths phase.
  • To analyze the behavior of density, survival probability, and local persistence in different phases.
  • To investigate the implications of continuously varying complex exponents.

Main Methods:

  • A one-dimensional model combining directed percolation and compact directed percolation rules.
  • Analysis of density decay, survival probability, and local persistence as functions of infection probability (p).
  • Investigation of critical phenomena at p=p_c and behavior for p>=p_s.

Main Results:

  • The model displays the Griffiths phase with algebraic density decay and continuously varying exponents.
  • In the active phase, memory loss is governed by continuously varying complex exponents.
  • Logarithmic periodic oscillations in persistence are observed due to complex exponents, with increasing amplitude and wavelength with p.

Conclusions:

  • The proposed model successfully replicates Griffiths phase behavior.
  • Complex exponents play a significant role in the dynamics of the active phase, leading to novel oscillatory phenomena.
  • The study highlights the importance of continuously varying exponents in understanding complex systems.