Breakdown of a renormalized perturbation expansion around mode-coupling theory of the glass transition

Abstract

PACS 64.70.Q--Theory and modeling of the glass transition PACS 64.70.P--Glass transitions of specific systems PACS 61.20.Lc -Time-dependent properties; relaxation Abstract -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.

Simple Theory for the Dynamics of Mean-Field-Like Models of Glass-Forming Fluids

“…The somewhat uncertain status of the mode-coupling theory resulting from its inadequacy in the largedimensional limit [15] is disappointing in view of the fact that attempts to go beyond a mean-field-like description of the dynamics usually start from the mode-coupling theory [16][17][18]. Parenthetically, we should note that most attempts to go beyond a mean-field-like static description of the glass transition use lattice-based effective Hamiltonians rather than particle-based models [19,20].…”