Contact Process — Absorbing State Transition

1D lattice near the DP critical point λc ≈ 3.297 — directed percolation universality

Parameters

Density ρ
λ_c (1D DP)≈ 3.297
Phase
Time0
Contact process (Harris 1974): each site is either active (1) or inactive (0).

• Active site → inactive at rate μ=1
• Active site → infects each neighbor at rate λ/2

Phase transition at λ_c ≈ 3.297 (1D). Below λ_c: activity dies out (absorbing state). Above λ_c: active phase with ρ > 0.

This belongs to the directed percolation (DP) universality class: β≈0.276, ν_⊥≈1.097, ν_‖≈1.734.

Space-time diagram: bright = active, dark = inactive. Watch clusters percolate.