  We use a linear system of Langevin spins with disordered interactions as an
exactly solvable toy model to investigate a procedure, recently proposed by
Coolen and Sherrington, for closing the hierarchy of macroscopic order
parameter equations in disordered spin systems. The closure procedure, based on
the removal of microscopic memory effects, is shown to reproduce the correct
equations for short times and in equilibrium. For intermediate time-scales the
procedure does not lead to the exact equations, yet for homogeneous initial
conditions succeeds at capturing the main characteristics of the flow in the
order parameter plane. The procedure fails in terms of the long-term temporal
dependence of the order parameters. For low energy inhomogeneous initial
conditions and near criticality (where zero modes appear) deviations in
temporal behaviour are most apparent. For homogeneous initial conditions the
impact of microscopic memory effects on the evolution of macroscopic order
parameters in disordered spin systems appears to be mainly an overall slowing
down.
