In the Achlioptas process, at each step two candidate edges are drawn and one is chosen by a rule. The product rule (minimize product of component sizes) suppresses giant component formation until a sudden explosive transition. Compare to random (Erdős-Rényi) percolation: the Achlioptas transition is far sharper and discontinuous-looking, though technically continuous with extreme finite-size effects.
ER percolation: continuous transition at t_c = N/2 edges
Giant component S ~ (t − t_c)^β, β=1 (ER mean field)
Product rule: suppresses giant until sudden jump
da Costa et al. 2010: truly discontinuous (first-order)?
Riordan-Wormald 2011: actually continuous but with β ≪ 1
Susceptibility χ = ⟨s²⟩ − ⟨s⟩² diverges at t_c