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

TL;DR

This paper critically examines a renormalized perturbation expansion around mode-coupling theory for the glass transition, revealing divergences at the transition point and proposing a re-summation that cancels the original predictions.

Contribution

It introduces a diagrammatic re-summation approach that exposes divergences and cancels the mode-coupling theory's irreducible memory function at the transition.

Findings

Divergences occur at the mode-coupling transition in the perturbation expansion.

A re-summation of ladder diagrams yields a finite result that cancels the original memory function.

The analysis challenges the validity of mode-coupling theory near the transition.

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.