Scaling and Renormalization Group in Replica Symmetry Breaking space: Evidence for a simple analytical solution of the SK model at zero temperature

Details Scaling and Renormalization Group in Replica Symmetry Breaking space: Evidence for a simple analytical solution of the SK model at zero temperature Scaling and Renormalization Group in Replica Symmetry Breaking space: Evidence for a simple analytical solution of the SK model at zero temperature

Publishing date

2005-09-27

URL

arxiv.org/abs/cond-mat/0509700v1

Science

Physics

Field

Condensed Matter

SubField

Disordered Systems and Neural Networks

Additional info

4 pages, 6 Figures, accepted for publication in Physical Review Letters

Type

Scientific paper

Digital Object Identifier

10.1103/PhysRevLett.95.197203

Abstract

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 non-trivial T->0-limit of the Parisi order function q(x) for the SK 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\leq a\leq infty where x/T->a at T=0 and \xi\approx 1.13\pm 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.

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