Related papers: Singular perturbation near mode-coupling transitio…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
The mode-coupling theory of the glass transition predicts the time evolution of the intermediate scattering functions in viscous liquids on the sole basis of the structural information encoded in two-point density correlations. We provide a…
Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the…
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry…
If the inflaton is a heavy scalar field, it may equilibrate slower than some other degrees of freedom, e.g. non-Abelian gauge bosons. In this case, perturbations in the inflaton field and in a thermal plasma coexist from a given moment…
Asymptotic stability is with no doubts an essential property to be studied for any system. This analysis often becomes very difficult for coupled systems and even harder when different timescales appear. The singular perturbation method…
The description of thermodynamic phase transitions in terms of percolation transitions of suitably defined clusters has a long tradition and boasts a number of important successes, the most prominent ones being in ferromagnetic lattice…
We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size which is typical of critical phenomena. Our approach is to introduce an external,…
A statistical mechanic study of the $XY$ model with nonlinear interaction is presented on bipartite sparse random graphs. The model properties are compared to those of the $p$-clock model, in which the planar continuous spins are…
We study the Langevin dynamics of a heteropolymer by means of a mode-coupling approximation scheme, giving rise to a set of coupled integro-differential equations relating the response and correlation functions. The analysis shows that…
We introduce and prove a novel linear response stability theory for spin glasses. The new stability under suitable perturbation of the equilibrium state implies the whole set of structural identities that characterize the spin glass phase.
We analyze the way in which duality constrains the exact beta function and correlation length in single-coupling spin systems. A consistency condition we propose shows very concisely the relation between self-dual points and phase…
Tipping points characterize situations where a regulated system may experience a sudden and irreversible change and are generally associated with a random state of the system below which the change materializes. In this paper, we study a…
The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is…
We study the long-time aging dynamics of spin-glass models with two-spin interactions by performing a Renormalization Group transformation on the time variable in the non-equilibrium dynamical generating functional. We obtain the RG…
The relaxation of Fourier modes of hamiltonian chains close to equilibrium is studied in the framework of a simple mode-coupling theory. Explicit estimates of the dependence of relevant time scales on the energy density (or temperature) and…
Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the…
We investigate the dynamics of a fluid of dipolar hard spheres in its liquid and glassy phase, with emphasis on the microscopic time or frequency regime. This system shows rather different glass transition scenarios related to its rich…
We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…
For a single scalar field with unit sound speed minimally coupled to Einstein gravity, there are exactly three distinct cosmological solutions which produce a scale invariant spectrum of curvature perturbations in a dynamical attractor…