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arXiv · 0902.1010

Singular perturbation near mode-coupling transition

Mami Iwata·Shin-ichi Sasa
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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.

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Mami Iwata, Shin-ichi Sasa. 2009-05-28. Singular perturbation near mode-coupling transition. https://doi.org/10.1088/1751-8113%2F42%2F24%2F245001

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