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Scaling and Renormalization Group in Replica-Symmetry-Breaking Space: Evidence for a Simple Analytical Solution of the Sherrington-Kirkpatrick Model at Zero Temperature

2005/09/27 by R. Oppermann, R.H. Oppermann, David C. Sherrington +1 · 2 citations
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.dis-nn

paper · pdf · doi:10.1103/physrevlett.95.197203

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

arxiv created 2005/09/27 · openalex publication_date 2005/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 nontrivial T\ensuremath→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)=\frac√\ensuremathπ2\fraca\ensuremathξ erf(\frac\ensuremathξa) on 0\ensuremath≤a\ensuremath≤\ensuremath∞, where (x)/(T)\ensuremath→a at T=0 and \ensuremathξ\ensuremath≈1.13\ifmmode±\else\textpm\fi0.01. \ensuremathξ 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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