Directed Percolation — Nonequilibrium Phase Transition

2D contact process at the DP universality class — absorbing phase transition with exact critical exponents β≈0.584, ν_⊥≈0.734

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Density ρ(t)

0.705

p_c (critical)

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Phase

Time step

Spreading prob p 0.705

Recovery rate q 0.40

Initial density ρ₀ 0.50

Display speed 3

Directed percolation (Janssen-Grassberger conjecture 1981/1982): any system with a single absorbing state, short-range interactions, and no extra symmetry belongs to the DP universality class. Critical point p_c ≈ 0.705 (2D contact process). Below p_c: absorbing state (extinction). Above p_c: active steady state. Exact exponents: β=0.584, ν_⊥=0.734, z=1.76.