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Field-theoretic analysis of directed percolation: Three-loop approximation.

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Directed bond percolation models critical phase transitions between active and absorbing states. This study uses field-theoretic and renormalization group methods to calculate critical exponents to third order.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Theory

Background:

  • The directed bond percolation model is fundamental in nonequilibrium statistical physics.
  • It describes continuous phase transitions between active and absorbing states.

Purpose of the Study:

  • To quantitatively describe the universality class of directed bond percolation.
  • To calculate critical exponents to the third order in perturbation theory.

Main Methods:

  • Field-theoretic formulation.
  • Renormalization group analysis.
  • Dimensional regularization with minimal subtraction scheme.
  • Perturbative calculations near the upper critical dimension (d=4).
  • Combination of analytical and numerical techniques to handle Feynman diagrams.

Main Results:

  • Calculation of critical exponents to the third order in perturbation theory.
  • Quantitative description of the directed bond percolation universality class.

Conclusions:

  • The study provides a high-order perturbative calculation of critical exponents for directed bond percolation.
  • The methods employed offer a robust framework for analyzing critical phenomena in similar models.