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We used a functional renormalization group method to study phase transitions in active systems. This approach accurately estimates critical exponents for directed percolation-type systems, even in low dimensions.

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Directed percolation describes systems transitioning between active and inactive states.
  • Understanding these phase transitions is crucial in various scientific fields.

Purpose of the Study:

  • To apply a functional renormalization group (fRG) approach to study the active-to-inactive phase transition.
  • To investigate systems where the transition is approached from the active, finite density phase.

Main Methods:

  • Developed a functional renormalization group approach.
  • Introduced a background field action functional by expanding the effective potential around its minimum.
  • Utilized nonperturbative flow equations derived from the fRG.

Main Results:

  • The fRG approach with a background field provides accurate estimates for critical exponents.
  • The method is effective even in low-dimensional systems.
  • Successfully characterized the active-to-inactive phase transition in directed percolation-type systems.

Conclusions:

  • The functional renormalization group is a powerful tool for studying critical phenomena in complex systems.
  • The background field method enhances the accuracy of fRG calculations for phase transitions.
  • This work provides valuable insights into the directed percolation universality class.