Singular perturbation near mode-coupling transition
arXiv:0902.1010 · doi:10.1088/1751-8113/42/24/245001
Abstract
We study the simplest mode-coupling equation which describes the time correlation function of the spherical p-spin glass model. We formulate a systematic perturbation theory near the mode-coupling transition point by introducing multiple time scales. In this formulation, the invariance with respect to the dilatation of time in a late stage yields an arbitrary constant in a leading order expression of the solution. The value of this constant is determined by a solvability condition associated with a linear singular equation for perturbative corrections in the late stage. The solution thus constructed provides exactly the alpha-relaxation time.
15 pages, 4 figures
References in corpus (5)
- Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
- Fluctuations in glassy systems
- Dynamics of k-core percolation in a random graph
- A theory for critically divergent fluctuations of dynamical events at non-ergodic transitions
- Scale-free patterns at a saddle-node bifurcation in a stochastic system