  We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the
presence of a magnetic field. The series expansion of the Parisi function
$q(x)$ is computed at high orders in powers of $\tau=T_c-T$ and $H$. We find
that none of the Parisi-Toulouse scaling hypotheses on the $q(x)$ behavior
strictly holds, although some of them are violated only at high orders. The
series is resummed yielding results in the whole spin-glass phase which are
compared with those from a numerical evaluation of the $q(x)$. At the high
order considered, the transition turns out to be third order on the
Almeida-Thouless line, a result which is confirmed rigorously computing the
expansion of the solution near the line at finite $\tau$. The transition
becomes smoother for infinitesimally small field while it is third order at
strictly zero field.
