Slow Dynamics in Glasses

We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a pure dynamical transition in some of these systems. We show how the results obtained for a random Hamiltonian may be also applied to a given Hamiltonian. These two results open the way to a better understanding of the glassy transition in real systems

Constraining massive gravity with recent cosmological data

A covariant formulation of a theory with a massive graviton and no negative energy state has been recently proposed as an alternative to the usual General Relativity framework. For a spatially flat homogenous and isotropic universe, the theory introduces modified Friedmann equations where the standard matter term is supplemented by four effective fluids mimicking dust, cosmological constant, quintessence and stiff matter, respectively. We test the viability of this massive gravity formulation by contrasting its theoretical prediction to the Hubble diagram as traced by Type Ia Supernovae (SNeIa) and Gamma Ray Bursts (GRBs), the $H(z)$ measurements from passively evolving galaxies, Baryon Acoustic Oscillations (BAOs) from galaxy surveys and the distance priors from the Cosmic Microwave Background Radiation (CMBR) anisotropy spectrum. It turns out that the model is indeed able to very well fit this large dataset thus offering a viable alternative to the usual dark energy framework. We finally set stringent constraints on its parameters also narrowing down the allowed range for the graviton mass.Comment: 10 pages, 1 figure, 2 tables, accepted for publication on Physical Review

Replica Symmetry Breaking in the Random Replicant Model

We study the statistical mechanics of a model describing the coevolution of species interacting in a random way. We find that at high competition replica symmetry is broken. We solve the model in the approximation of one step replica symmetry breaking and we compare our findings with accurate numerical simulations.Comment: 12 pages, TeX, 5 postscript figures are avalaible upon request, submitted to Journal of Physics A: Mathematical and Genera

4D Spin Glasses in Magnetic Field Have a Mean Field like Phase

By using numerical simulations we show that the 4D $J=\pm 1$ Edwards Anderson spin glass in magnetic field undergoes a mean field like phase transition. We use a dynamical approach: we simulate large lattices (of volume $V$) and work out the behavior of the system in limit where both $t$ and $V$ go to infinity, but where the limit $V \to \infty$ is taken first. By showing that the dynamic overlap $q$ converges to a value smaller than the static one we exhibit replica symmetry breaking. The critical exponents are compatible with the ones obtained by mean field computations.Comment: Physrev format, 5 ps figures include

Off-Equilibrium Effective Temperature in Monatomic Lennard-Jones Glass

The off-equilibrium dynamics of a monatomic Lennard-Jones glass is investigated after sudden isothermal density jumps (crunch) from well equilibrated liquid configurations towards the glassy state. The generalized fluctuation-dissipation relation has been studied and the temperature dependence of the violation factor m is found in agreement with the one step replica symmetry breaking scenario, i.e. at low temperature m(T) is found proportional to T up to an off-equilibrium effective temperature T_eff, where m(T_eff)=1. We report T_eff as a function of the density and compare it with the glass transition temperatures T_g as determined by equilibrium calculations.Comment: 4 pages,4 figure

The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results

The mathematically correct computation of the spin glasses free energy in the infinite range limit crowns 25 years of mathematic efforts in solving this model. The exact solution of the model was found many years ago by using a heuristic approach; the results coming from the heuristic approach were crucial in deriving the mathematical results. The mathematical tools used in the rigorous approach are quite different from those of the heuristic approach. In this note we will review the heuristic approach to spin glasses in the light of the rigorous results; we will also discuss some conjectures that may be useful to derive the solution of the model in an alternative way.Comment: 12 pages, 1 figure; lecture at the Flato Colloquia Day, Thursday 27 November, 200

Magnetic field chaos in the SK Model

We study the Sherrington--Kirkpatrick model, both above and below the De Almeida Thouless line, by using a modified version of the Parallel Tempering algorithm in which the system is allowed to move between different values of the magnetic field h. The behavior of the probability distribution of the overlap between two replicas at different values of the magnetic field h_0 and h_1 gives clear evidence for the presence of magnetic field chaos already for moderate system sizes, in contrast to the case of temperature chaos, which is not visible on system sizes that can currently be thermalized.Comment: Latex, 16 pages including 20 postscript figure

Renormalization Group Approach to Spin Glass Systems

A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining transformation, that is performed on the overlap probability measure (which is clearly non-Gibbsian). Universality classes are thus naturally defined on a large set of models, going from $\Z_2$ and Gaussian spin glasses to Ising and fully frustrated models, and others.Comment: 12 pages, 4 figure