Related papers: Saddle Points Stability in the Replica Approach Of…
We introduce a three replica potential useful to examine the structure of metastables states above the static transition temperature, in the spherical p-spin model. Studying the minima of the potential we are able to find which is the…
Recent numerical developments in the study of glassy systems have shown that it is possible to give a purely geometric interpretation of the dynamic glass transition by considering the properties of unstable saddle points of the energy.…
Within the replica approach to mean-field spin-glasses the transition from ergodic high-temperature behaviour to the glassy low-temperature phase is marked by the instability of the replica-symmetric saddle-point. For general spin-glass…
In this talk we review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
In these two lectures I review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence…
In this paper we study the on and off-equilibrium properties of the four dimensional Gaussian spin glass. In the static case we determine with more precision that in previous simulations both the critical temperature as well as the critical…
We perform the replica symmetry breaking (RSB) in the vicinity of the point of instability of the replica symmetric solution in the model of axial quadrupolar glass. It is shown that the solution with the first stage RSB is stable against…
In this paper we develop a method introduced by one of us to study metastable states in spin glasses. We consider a `potential function' defined as the free energy of a system at a given temperature $T$ constrained to have a fixed overlap…
By numerical simulations of the $3d$ Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.
According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to…
We study partially occupied lattice systems of classical magnetic dipoles which point along randomly oriented axes. Only dipolar interactions are taken into account. The aim of the model is to mimic collective effects in disordered…
We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which…
The Complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising $p$-spin is investigated in the temperature regime where the equilibrium phase is one step Replica Symmetry Breaking. Two solutions of the resulting saddle point…
We show that the only solutions of the TAP equations for the Sherrington-Kirkpatrick model of Ising spin glasses which can be found by iteration are those whose free energy lies on the border between replica symmetric and broken replica…
A model glass with fast and slow processes is studied. The statics is simple and the facilitated slow dynamics is exactly solvable. The main features of a fragile glass take place: Kauzmann transition, Vogel-Fulcher law, Adam-Gibbs relation…
We present a critical analysis of the Sompolinsky theory of equilibrium dynamics. By using the spherical $2+p$ spin glass model we test the asymptotic static limit of the Sompolinsky solution showing that it fails to yield a…
We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from antiferromagnetic to spin glass state. The eigenvalues associated with replica-symmetric…
We study the off equilibrium dynamics of a mean field disordered systems which can be interpreted both as a long range interaction spin glass and as a particle in a random potential. The statics of this problem is well known and exhibits a…
A model is derived for the viscoelastic response of glasses at isothermal uniaxial deformation with small strains. A glass is treated as an ensemble of relaxing units with various activation energies for rearrangement. With reference to the…