interpolation of the $11$-RSB solution. In particular it confirms the approximate scaling $q(x,T)\sim q(x/T)$ at low temperatures, see Figure \[fig:rqxpad\]. Note that the scaling fails when $\beta x\sim O(1)$, in agreement with the findings of previous section.

Finally we mention that an alternative resummation technique based on the Borel transform give results consistent with those obtained with the Padè approximants.

Numerical Integration of the $\infty$-RSB equations {#SecNum}
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To check the analytical results of the previous sections we have solved numerically the $\infty$-RSB equations (\[SP1\]) - (\[condP\]) on a discrete set of points in the infinite strip $[0\leq x\leq 1$; $-\infty< y <\infty]$ and determined $q(x)$, $P(x,y)$ and $m(x,y)$. The numerical method is based on the iterative procedure of Ref. [@topomoto]: from an initial guess of $q(x)$ the fields $m(x,y)$, $P(x,y)$ and the associated $q(x)$ are computed in order as:

1.  Compute $m(x,y)$ integrating from $x=x_0$ to $x=0$ eqs. (\[SP2\]) with initial condition (\[condm\]).

2.  Compute $P(x,y)$ integrating from $x=0$ to $x=x_0$ eqs. (\[SP3\]) with initial condition (\[condP\]).

3.  Compute $q(x)$ using eq. (\[SP1\]).

where $x_0\leq 1$ (See later). The steps $1.\,\to\, 2.\,\to\, 3.$ are repeated until a reasonable convergence is reached, typically mean square error on $q$, $P$ and 