Contact Process — Directed Percolation

The contact process models epidemic spreading on a 1D lattice. Sites are active (infected) or inactive (recovered). Near the critical infection rate λ_c ≈ 3.298, the system undergoes a continuous phase transition in the directed percolation universality class.

Parameters

Density: —
Time: 0
Phase: —
Critical point: λ_c/δ ≈ 3.298
Order param: ρ ~ (λ-λ_c)^β
β ≈ 0.2765 (DP universality)
ξ_⊥ ~ |λ-λ_c|^{-ν_⊥}, ν_⊥≈1.097
ξ_∥ ~ |λ-λ_c|^{-ν_∥}, ν_∥≈1.734

Phase Diagram