2016/12/31 by Malo Tarpin, Federico Benitez, Léonie Canet +1 · 19 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Critical exponent #Directed percolation #Fixed point #Homogeneous space #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Phase transition #Physics #Population #Quantum mechanics #Renormalization #Renormalization group #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.96.022137
published in Physical review. E 96(2), 022137 (American Physical Society) · 12 pages, 2 figures, some corrections
openalex publication_date 2017/08/16 · arxiv created 2017/08/28 · arxiv updated 2017/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the Diffusive Epidemic Process (DEP), a two-species reaction-diffusion process originally proposed to model disease spread within a population. This model exhibits a phase transition from an active epidemic to an absorbing state without sick individuals. Field-theoretic analyses suggest that this transition belongs to the universality class of Directed Percolation with a Conserved quantity (DP-C, not to be confused with conserved-directed percolation C-DP, appearing in the study of stochastic sandpiles). However, some exact predictions derived from the symmetries of DP-C seem to be in contradiction with lattice simulations. Here we revisit the field theory of both DP-C and DEP. We discuss in detail the symmetries present in the various formulations of both models. We then investigate the DP-C model using the derivative expansion of the nonperturbative renormalization group formalism. We recover previous results for DP-C near its upper critical dimension dc=4, but show how the corresponding fixed point seems to no longer exist below d≲3. Consequences for the DEP universality class are considered.