2005/12/12 by Sergey Pankov · 2 citations
Engineering · Materials Science · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.96.197204
published as Phys. Rev. Lett. 96, 197204 (2006) · 4 pages, 4 figures
arxiv created 2005/12/12 · openalex publication_date 2006/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I propose a simple scaling ansatz for the full replica symmetry breaking solution of the Sherrington-Kirkpatrick model in the low energy sector. This solution is shown to become exact in the limit x --> 0, Bx --> infinity of the Parisi replica symmetry breaking scheme parameter . The distribution function of the frozen fields has been known to develop a linear gap at zero temperature. The scaling equations are integrated to find an exact numerical value for the slope of the gap thetaP(x,y)/delta|(y --> 0) = 0.301 046.... I also use the scaling solution to devise an inexpensive numerical procedure for computing finite time scale (x =1) quantities. The entropy, the zero field cooled susceptibility, and the local field distribution function are computed in the low-temperature limit with high precision, barely achievable by currently available methods.