Real Space Renormalization Group Theory of Disordered Models of Glasses

Abstract

We develop a real space renormalisation group analysis of disordered models of glasses, in particular of the spin models at the origin of the Random First Order Transition theory. We find three fixed points respectively associated to the liquid state, to the critical behavior and to the glass state. The latter two are zero-temperature ones; this provides a natural explanation of the growth of effective activation energy scale and the concomitant huge increase of relaxation time approaching the glass transition. The lower critical dimension depends on the nature of the interacting degrees of freedom and is higher than three for all models. This does not prevent three dimensional systems from being glassy. Indeed, we find that their renormalisation group flow is affected by the fixed points existing in higher dimension and in consequence is non-trivial. Within our theoretical framework the glass transition results to be an avoided phase transition.

6 pages, 3 figures

References in corpus (11)

• Theoretical perspective on the glass transition and amorphous materials
• Rigorous Inequalities between Length and Time Scales in Glassy Systems
• Breakdown of Elasticity in Amorphous Solids
• Exact theory of dense amorphous hard spheres in high dimension. I. The free energy
• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
• Constructing explicit magnetic analogies for the dynamics of glass forming liquids
• Origin of the Growing Length Scale in M-p-Spin Glass Models
• Critical properties of the four-state Commutative Random Permutation Glassy Potts model in three and four dimensions
• Mosaic length and finite interaction-range effects in a one dimensional random energy model
• Evidence of one-step replica symmetry breaking in a three-dimensional Potts glass model
• The Super-Potts glass: a new disordered model for glass-forming liquids

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