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We quantitatively studied the general epidemic process, a model in nonequilibrium statistical physics. Our research determined the critical dynamic exponent (z) to the three-loop approximation for the dynamic isotropic percolation class.

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • The general epidemic process is a key model in nonequilibrium statistical physics.
  • It exhibits continuous phase transitions between active and absorbing states.
  • Its universal properties are described by the dynamic isotropic percolation universality class.

Purpose of the Study:

  • To quantitatively study the dynamic isotropic percolation universality class.
  • To determine the critical dynamic exponent (z) to the three-loop approximation.
  • To finalize the quantitative description of this universality class.

Main Methods:

  • Field-theoretic formulation of the general epidemic process model.
  • Perturbative renormalization-group analysis.
  • Dimensional regularization with the minimal subtraction scheme.

Main Results:

  • The critical dynamic exponent (z) was calculated to the three-loop approximation.
  • Perturbative expansions were performed in terms of ɛ = 6 - d, where d is the dimension and d_c = 6 is the upper critical dimension.

Conclusions:

  • The study provides a precise quantitative description of the dynamic isotropic percolation class.
  • The findings advance the understanding of phase transitions in nonequilibrium statistical physics.
  • The three-loop approximation offers a refined calculation of the critical dynamic exponent (z).