Directed Percolation — Absorbing Phase Transition

A paradigmatic non-equilibrium phase transition. Activity spreads forward in time with probability p. Below p_c, it dies out (absorbing state). Above p_c, it survives forever. No going back once absorbed.

Parameters

Activity density: --

DP Universality Class

p_c ≈ 0.6447 (1D DP)

Near p_c:
ρ ~ (p−p_c)^β, β≈0.276
ξ_⊥ ~ |p−p_c|^{-ν_⊥}, ν_⊥≈1.097
ξ_∥ ~ |p−p_c|^{-ν_∥}, ν_∥≈1.734

Colored = active
Black = absorbed forever

Key Physics

DP class: any model with a single absorbing state + no conservation law. Epidemics, turbulence onset, neural avalanches all belong to this class (Janssen-Grassberger conjecture).