Renormalization Group Analysis of the Random First-Order Transition

Renormalization group analysis of the random first-order transition.

We consider the approach describing glass formation in liquids as a progressive trapping in an exponentially large number of metastable states. To go beyond the mean-field setting, we provide a real-space renormalization group (RG) analysis of the associated replica free-energy functional. The present approximation yields in finite dimensions an ideal glass transition similar to that found in t...

Autoregressive Gaussian Random Vectors of First Order

The Exact Renormalization Group and First-order Phase Transitions

Studies of first-order phase transitions through the use of the exact renormalization group are reviewed. In the first part the emphasis is on universal aspects: We discuss the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields – the cubic anisotropy model. In the second part we review the application of the exact re...

Renormalization-Group Study of Weakly First-Order Phase Transitions

We study the universal critical behavior near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields – the cubic anisotropy model. Renormalization-group techniques are employed within the formalism of the effective average action. We calculate the coarse-grained free energy and deduce the universal ratio of susceptibilities on either side of the phase tr...

Random pinning glass transition: hallmarks, mean-field theory and renormalization group analysis.

We present a detailed analysis of glass transitions induced by pinning particles at random from an equilibrium configuration. We first develop a mean-field analysis based on the study of p-spin spherical disordered models and then obtain the three-dimensional critical behavior by the Migdal-Kadanoff real space renormalization group method. We unveil the important physical differences with the c...