Contact Process: Directed Percolation

1+1D spacetime diagram — infection spreads, recovers, and either survives or dies

Time: 0
Density ρ: 0.000
λ: 3.298
Phase: Critical
The contact process is a paradigm for Directed Percolation (DP) universality. Each infected site (white) spreads to neighbors at rate λ and recovers at rate 1. Below λc ≈ 3.298: absorbing (dead) state inevitable. Above λc: active phase survives forever with positive density. At λc: scale-invariant clusters, critical exponents β ≈ 0.276, ν ≈ 1.097.