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.

• Received 23 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.064204