Breakdown of a renormalized perturbation expansion around mode-coupling theory of the glass transition
1 Department of Chemistry, Colorado State University - Fort Collins, CO 80523, USA
2 Yukawa Institute for Theoretical Physics, Kyoto University - Kyoto 606-8502, Japan
Received: 23 May 2013
Accepted: 6 September 2013
We analyze a renormalized perturbation expansion around the mode-coupling theory of the glass transition. We focus on the long-time limit of the irreducible memory function. We discuss a renormalized diagrammatic expansion for this function and re-sum two infinite classes of diagrams. We show that the resulting contributions to the irreducible memory function diverge at the mode-coupling transition. A further re-summation of ladder diagrams constructed by iterating these divergent contributions gives a finite result which cancels the mode-coupling theory's expression for the irreducible memory function.
PACS: 64.70.Q- – Theory and modeling of the glass transition / 64.70.P- – Glass transitions of specific systems / 61.20.Lc – Time-dependent properties; relaxation
© EPLA, 2013