L. F. Cugliandolo

Learn More
35 where the expectation value is deened by hA(x)i = R dx e ?x 2 p 2 cosh m (p 2x)A(x) R dx e ?x 2 p 2 cosh m (p 2x) : (62) Inserting in (56) this value of we have searched among the 5 values of g the one which gives the maximum free energy when the stability is marginal (i.e. when (56) is saturated). We have found that the eigenvalue g 5 is the one which(More)
We analyse the Langevin dynamics of the random walk, the scalar field, the X-Y model and the spinoidal decomposition. We study the deviations from the equilibrium dynamics theorems (FDT and homogeneity), the asymptotic behaviour of the systems and the aging phenomena. We compare the results with the dynamical behaviour of (random) spin-glass mean-field(More)
These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario for this temporal evolution derived from the solution to some solvable models (p spin and the like) that are intimately connected to the mode(More)
We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations of short-range spin glasses. Local fluctuations and responses are shown to be connected by a generalized local(More)
We study the non-equilibrium relaxation of the spherical spin-glass model with p-spin interactions in the N → ∞ limit. We analytically solve the asymptotics of the magnetization and the correlation and response functions for long but finite times. Even in the thermodynamic limit the system exhibits ‘weak’ (as well as ‘true’) ergodicity breaking and aging(More)
Figure 4: The value of the breakpoint m in the replica symmetry breaking solution for soft spheres as a function of the dimensionless density. Figure 3: The correlations ~ g(r) (full line) and g 1 (r) (broken line) obtained from the repli-cated hnc equations, as functions of the distance, for soft spheres at the density where replica symmetry is broken (=(More)
We show that, in nonequilibrium systems with small heat flows, there is a time-scale dependent effective temperature which plays the same role as the thermodynamical temperature, in that it controls the direction of heat flows and acts as a criterion for thermalization. We simultaneously treat the case of stationary systems with weak stirring and of glassy(More)
We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering systems during an infinitely slow annealing across a second-order phase transition. We elucidate the time and cooling rate dependence of the typical growing length, and we use it to predict the number of topological defects left over in the symmetry broken phase as a function(More)
In this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of models(More)