Another phase transition occurs when Σ Σ ( s ∗ ∗ ) = 0 , that is, α α = α α c := p ( 2 − − p ) + log 2 ⁡ ⁡ ( 2 − − p ) When α α > α α c , the optimal entropy density becomes unreachable, as there almost surely exists zero clusters with entropy density s ∗ ∗ . Instead, the state space is dominated by clusters with entropy close to s c , the larger solution to Σ Σ ( s c ) = 0 .