  A method is provided to compute the parameter exponent $\lambda$ yielding the
dynamic exponents of critical slowing down in mode coupling theory. It is
independent from the dynamic approach and based on the formulation of an
effective static field theory. Expressions of $\lambda$ in terms of third order
coefficients of the action expansion or, equivalently, in term of six point
cumulants are provided. Applications are reported to a number of mean-field
models: with hard and soft variables and both fully-connected and dilute
interactions. Comparisons with existing results for Potts glass model, ROM,
hard and soft-spin Sherrington-Kirkpatrick and p-spin models are presented.

Disordered Systems and Neural Networks;Statistical Mechanics