Scaling and renormalization group in replica-symmetry-breaking space: evidence for a simple analytical solution of the Sherrington-Kirkpatrick model at zero temperature.
Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB steps playing a role of decimation scales, we report evidence for a nontrivial T-->0 limit of the Parisi order function q(x) for the Sherrington-Kirkpatrick spin glass. Supported by scaling in RSB space, the fixed point order function is conjectured to be q*(a)=sqrt[pi]/2 a/xi erf(xi/a) on 0<or=a<or=infinity, where x/T --> a at T =0 and xi approximately 1.13+/-0.01. Xi plays the role of a correlation length in a-space. q*(a) may be viewed as the solution of an effective 1D field theory.
Oppermann
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Institut für Theoretische Physik, Universität Würzburg, Am Hubland, 97074 Würzburg, Federal Republic of Germany.
Sherrington
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