Approximating the Gibbs Measure of Spherical Spin Glasses to Within $o(N^{-1/2})$ in the Replica Symmetric Phase

We study the magnetization vector of mixed spherical spin glasses in a weak external field, in the replica symmetric phase. We derive a coordinatewise expansion of the magnetization which includes the leading cubic correction to the quadratic approximation, with an error that is $o(N^{-1/2})$ per co