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We study two dimensional frustrated but non-disordered systems applying a replica approach to a stripe forming model with competing interactions. The phenomenology of the model is representative of several well known systems, like high-Tc…
In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…
The variational principle (VP) has been used to capture the metastable states of a glass-forming molecular system without quenched disorder. It has been shown that VP naturally leads to a self-consistent random field Ginzburg-Landau model…
This thesis sums up the research work I performed as a PhD student in Sapienza Universit\`a di Roma, and \'Ecole Normale Sup\'erieure, Paris, under the joint supervision of Prof. Giorgio Parisi and Dr. Francesco Zamponi. The thesis focuses…
Using our previous results for the configurational entropy of a stripe glass as well as a variational result for the bare surface tension of entropic droplets we show that there is no disagreement between the numerical simulations of…
A Collision-Avoiding flocking particle system proposed in [8] is studied in this paper. The global wellposedness of its corresponding Vlasov-type kinetic equation is proved. As a corollary of the global stability result, the mean field…
This lecture deals with glassy dynamics and aging in disordered systems. Special emphasis is put on dynamic mean field theory. In the first part I present some of the systems of interest, in particular spin-glasses, supercooled liquids and…
Glassy polymer melts such as the plastics used in pipes, structural materials, and medical devices are ubiquitous in daily life. They accumulate damage over time due to their use, which limits their functionalities and demands periodic…
In this paper, we study general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, the existence and uniqueness of local and global solutions are proved with some new ideas for a…
We show the existence of intermittent dynamics in one of the simplest model of a glassy system: the two-state model, which has been used to explain the origin of the violation of the fluctuation-dissipation theorem. The dynamics is analyzed…
We show that the replica approach to glassy dynamics provides, in spite of its static nature, a characterization of critical dynamics in the $\beta$-regime of super-cooled liquids that is equivalent to the one of Mode-Coupling-Theory, both…
Glasses at low temperature fluctuate around their inherent states; glassy anomalies reflect the structure of these states. Recently there have been numerous observations of long-range stress correlations in glassy materials, from…
We study the mean-field phase diagram of glassy systems in a field pointing in the direction of a metastable state. We find competition among a ``magnetized'' and a ``disordered'' phase, that are separated by a coexistence line as in…
Using a novel self-consistent implementation of Hedin's GW perturbation theory we calculate space and energy dependent self-energy for a number of materials. We find it to be local in real space and rapidly convergent on second-- to third--…
Loss functions with non-isolated minima have emerged in several machine learning problems, creating a gap between theory and practice. In this paper, we formulate a new type of local convexity condition that is suitable to describe the…
The gauge principle as applied in field theories for particle physics recognizes redundant degrees of freedom. Some time ago this author introduced a frustration based locally preferred structure (LPS) model of the glass transition. Here we…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
On the example of a real scalar field, an approach to quantization of non-linear fields and construction of the perturbation theory with account of spontaneous symmetry breaking is proposed. The method is based on using as the main…
We provide a compact derivation of the static and dynamic equations for infinite-dimensional particle systems in the liquid and glass phases. The static derivation is based on the introduction of an "auxiliary" disorder and the use of the…
We investigate the p-state mean-field model of the Potts glass ($2\le p \le 4$) below the continuous phase transition to a glassy phase. We find that apart from a solution with a first hierarchical level of replica-symmetry breaking (1RSB),…