Low-temperature solution of the Sherrington-Kirkpatrick model

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, beta x ->infinity of the Parisi replica symmetry breaking scheme parameter x. The distribution function P(x,y) of the frozen fields y 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 partial derivative P(x,y)/partial derivative y parallel to(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.