moreover applied often to reduced forms $\infty$-replica symmetry breaking equations valid only near the critical temperature. From the numerical point of view there are only few works which confirm the general properties of the solution but do not allow for high accuracy. On the other hand $\infty$-replica symmetry breaking solutions of the type encountered in the SK model have been found in other models of interest in different fields, e.g., in computer science with solvability problems [@Luca] or in the study of the structural glass transition [@G85; @KT87; @SNA97].

Motivated by these problems we believe that it would be quite useful to have some reliable and efficient tool to find good approximations of the full solution also far from the critical points. In this work we reconsider two approaches. The first one is based on expansions for temperatures near the critical temperature $T_c$. As said above previous works considered only low order expansions [@P7980; @K83; @S85]. Here, by using algebraic manipulators, we push the expansion to rather high orders and resumming it via Padè resummation technique we are able to a have good estimate of the solution for a wide range of temperature below $T_c$.

The second approach is numerical. 