  We consider the problem of solving TAP mean field equations by iteration for
Ising model with coupling matrices that are drawn at random from general
invariant ensembles. We develop an analysis of iterative algorithms using a
dynamical functional approach that in the thermodynamic limit yields an
effective dynamics of a single variable trajectory. Our main novel contribution
is the expression for the implicit memory term of the dynamics for general
invariant ensembles. By subtracting these terms, that depend on magnetizations
at previous time steps, the implicit memory terms cancel making the iteration
dependent on a Gaussian distributed field only. The TAP magnetizations are
stable fixed points if an AT stability criterion is fulfilled. We illustrate
our method explicitly for coupling matrices drawn from the random orthogonal
ensemble.
