Functional form of the Parisi overlap distribution for the three-dimensional Edwards-Anderson Ising spin glass

Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated systems. For certain probability densities this predicts the characteristic large x falloff behavior f(x) approximately exp(-ae(x)), a>0. Using a multicanonical Monte Carlo technique, we have measured the Parisi overlap distribution P(q) for the three-dimensional Edward-Anderson Ising spin glass at and below the critical temperature We find that a probability distribution related to extreme-order statistics gives an excellent description of P(q) over about 80 orders of magnitude.