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)=√π2aξ erf(ξa) on 0≤a≤∞, where x/T→a at $T=0$ and ξ≈1.13±0.01. ξ plays the role of a correlation length in a-space. q*(a) may be viewed as the solution of an effective $1D$ field theory.