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Nonperturbative renormalization group for the diffusive epidemic process.

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We investigated the Diffusive Epidemic Process (DEP) and its relation to Directed Percolation with a Conserved quantity (DP-C). Our findings challenge existing theories, suggesting DP-C

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Area of Science:

  • Statistical Physics
  • Mathematical Biology
  • Complex Systems

Background:

  • The Diffusive Epidemic Process (DEP) models disease spread using a two-species reaction-diffusion framework.
  • DEP exhibits a phase transition from an active epidemic to an absorbing state.
  • Field theory suggests this transition aligns with the Directed Percolation with a Conserved quantity (DP-C) universality class.

Purpose of the Study:

  • To re-examine the field theory of DP-C and DEP.
  • To investigate discrepancies between DP-C theoretical predictions and lattice simulations.
  • To clarify the symmetries and universality class of the DEP model.

Main Methods:

  • Detailed analysis of symmetries in DP-C and DEP formulations.
  • Application of the derivative expansion within the nonperturbative renormalization group formalism to DP-C.
  • Comparison of theoretical results with existing lattice simulation data.

Main Results:

  • Recovered known results for DP-C near its upper critical dimension (d_c=4).
  • Demonstrated that the DP-C fixed point appears to vanish for dimensions below approximately 3 (d≲3).
  • Identified potential issues with the DP-C universality class assignment for DEP.

Conclusions:

  • The standard field-theoretic description of DP-C may not fully capture the behavior of DEP, especially in lower dimensions.
  • The observed breakdown of the DP-C fixed point below d≲3 has significant implications for understanding epidemic models.
  • Further theoretical and computational studies are needed to resolve the universality class of the Diffusive Epidemic Process.