Critical slowing down exponents in structural glasses: Random orthogonal and related models

An important prediction of mode-coupling theory is the relationship between the power-law decay exponents in the beta regime and the consequent definition of the so-called exponent parameter lambda. In the context of a certain class of mean-field glass models with quenched disorder, the physical meaning of lambda has recently been understood, yielding a method to compute it exactly in a static framework. In this paper we exploit this new technique to compute the critical slowing down exponents for such models including, as special cases, the Sherrington-Kirkpatrick model, the p-spin model, and the random orthogonal model.