About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass

Details About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass

2001-08-02

arxiv.org/abs/cond-mat/0108034v1

Phys. Rev. E65, 045102R 2002

Physics

Condensed Matter

Statistical Mechanics

4 pages RevTex, 3 figures

Scientific paper

10.1103/PhysRevE.65.045102

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

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