Directed Percolation — DP Universality Class

Active

Inactive

Critical seed

Space → horizontal · Time → downward

Parameters

Bond prob. p 0.645 Width 200 Speed 20 rows/frame

Order Parameter

Active density ρ—

Time step0

Phase—

p_c (1D DP)≈ 0.6447

DP Critical Exponents

β (order param.)0.276

ν∥ (time corr.)1.734

ν⊥ (space corr.)1.097

δ (survival exp.)0.159

z = ν∥/ν⊥1.581

About

Directed percolation is the canonical universality class for absorbing-state transitions. Sites activate neighbors with probability p. Below p_c, activity dies; above it, a percolating active cluster survives. The transition is continuous with universal exponents described by Reggeon field theory (Janssen 1981, Grassberger 1982).