Scaling and renormalization group in replica-symmetry-breaking space: evidence for a simple analytical solution of the Sherrington-Kirkpatrick model at zero temperature.

Journal article

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 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.

Authors: Oppermann, R; Sherrington, D

• Publication status: Published
• Journal: Physical Review Letters
• Volume: 95
• Issue: 19
• Pages: 197203
• Publication date: 2005-11-01
• DOI: 10.1103/physrevlett.95.197203
• EISSN: 1079-7114
• ISSN: 0031-9007
• Language: English