Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental verifications.

The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It...

In this work we study the nonequilibrium dynamical properties of an ultra-thin magnetic film model. Previous works on this system revealed the presence of novel dynamical properties that were difficult to interpret within a single physical scenario: on one hand the analysis of the aging...

A new handshake scheme is presented for tight-binding (TB) and molecular dynamics (MD) for multi-scale simulation of covalent crystals. In the present scheme, when calculating the forces on MD atoms in the handshake region, the TB atoms in close proximity to the MD atoms are treated as MD...

A numerical method is proposed in order to track field lines of three-dimensional divergence free fields. Field lines are computed by a locally valid Hamiltonian mapping, which is computed using a symplectic scheme. The method is theoretically valid everywhere but at points where the field is...

This paper compares three different types of “onset of chaos” in the logistic and generalized logistic map: the Feigenbaum attractor at the end of the period doubling bifurcations; the tangent bifurcation at the border of the period three window; the transition to chaos in the generalized...

Quantum characteristics of the Topological Non-connectivity Threshold (TNT), introduced in [F. Borgonovi, G.L. Celardo, M. Maianti, E. Pedersoli, J. Stat. Phys. <Emphasis Type="Bold">116, 516 (2004)], have been analyzed in the hard quantum regime. New interesting perspectives in term of the possibility to study the...</emphasis>

We review, with emphasis on the dynamical point of view, the classical characteristics of the Topological Nonconnectivity Threshold (TNT), recently introduced in F. Borgonovi, G.L. Celardo, M. Maianti and E. Pedersoli, J. Stat. Phys. <Emphasis Type="Bold">116, 1435 (2004). This shows interesting connections among...</emphasis>

The relation between the Lyapunov modes (delocalized Lyapunov vectors) and the momentum autocorrelation function is discussed in two-dimensional hard-disk systems. We show numerical evidence that the smallest time-oscillating period of the Lyapunov modes is twice as long as the time-oscillating...