When β β < β β c , the system is not in the condensed phase, and so by asymptotic equipartition, the Boltzmann distribution is asymptotically uniformly distributed over ∼ ∼ e N ( ln ⁡ ⁡ 2 − − β β 2 / 4 ) states. The participation ratio is then ∼ ∼ e N ( ln ⁡ ⁡ 2 − − β β 2 / 4 ) × × ( e − − N ( ln ⁡ ⁡ 2 − − β β 2 / 4 ) ) 2 = e − − N ( ln ⁡ ⁡ 2 − − β β 2 / 4 ) which decays exponentially to zero.