  The high-order behavior of the perturbation expansion in the cubic replica
field theory of spin glasses in the paramagnetic phase has been investigated.
The study starts with the zero-dimensional version of the replica field theory
and this is shown to be equivalent to the problem of finding finite size
corrections in a modified spherical spin glass near the critical temperature.
We find that the high-order behavior of the perturbation series is described,
to leading order, by coefficients of alternating signs (suggesting that the
cubic field theory is well-defined) but that there are also subdominant terms
with a complicated dependence of their sign on the order. Our results are then
extended to the d-dimensional field theory and in particular used to determine
the high-order behavior of the terms in the expansion of the critical exponents
in a power series in epsilon=6-d. We have also corrected errors in the existing
epsilon expansions at third order.
