Related papers: Saddle Points Stability in the Replica Approach Of…
Numerical simulations demonstrate a link between dynamically cold initial solutions and self-similarity. However the nature of this link is not fully understood. Cold initial conditions alone without further symmetry do not lead to…
The nature of the spin glass state is investigated by studying changes to the ground state when a weak perturbation is applied to the bulk of the system. We consider short range models in three and four dimensions and the infinite range…
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…
Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs…
Saddle fixed points are the centerpieces of complicated dynamics in a system. The one-dimensional stable and unstable manifolds of these saddle-points are crucial to understanding the dynamics of such systems. While the problem of sketching…
Systems of globally coupled logistic maps (GCLM) can display complex collective behaviour characterized by the formation of synchronous clusters. In the dynamical clustering regime, such systems possess a large number of coexisting…
In these lectures I will review the approach to glasses based on the replica formalism. Many of the physical ideas are very similar to those of older approaches. The replica approach has the advantage of describing in an unified setting…
We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy phase. We briefly review the present theoretical understanding of the spectacular phenomena observed in experiments and describe new numerical results obtained in…
We review the approach to glasses based on the replica formalism. The replica approach presented here is a first principle's approach which aims at deriving the main glass properties from the microscopic Hamiltonian. In contrast to the old…
After briefly describing the present status of the spin glass theory, we present a conjecture on the exact location of the multicritical point in the phase diagram of finite-dimensional spin glasses. The theory enables us to understand in a…
In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
For a general class of saddle point problems sharp estimates for Babu\v{s}ka's inf-sup stability constants are derived in terms of the constants in Brezzi's theory. In the finite-dimensional Hermitian case more detailed spectral properties…
Despite the extreme simplicity in their definition, spin glasses disclose a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis we try to shed light on some of them, focusing on one hand on the search of…
In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the…
Attitude control systems naturally evolve on nonlinear configuration spaces, such as S^2 and SO(3). The nontrivial topological properties of these configuration spaces result in interesting and complicated nonlinear dynamics when studying…
For large but finite systems the static properties of the infinite ranged Sherrington-Kirkpatrick model are numerically investigated in the entire the glass regime. The approach is based on the modified Thouless-Anderson-Palmer equations in…
The study of the properties of glass-forming liquids is difficult for many reasons. Analytic solutions of mean field models are usually available only for systems embedded in a space with an unphysically high number of spatial dimensions;…
A review of the stochastic stability property for the Gaussian spin glass models is presented and some perspectives discussed.
A three-dimensional $\pm J$ XY spin-glass model is investigated by a nonequilibrium relaxation method. We have introduced a new criterion for the finite-time scaling analysis. A transition temperature is obtained by a crossing point of…