Exact mean field inference in asymmetric kinetic Ising systems

We develop an elementary mean field approach for fully asymmetric kinetic Ising models, which can be applied to a single instance of the problem. In the case of the asymmetric SK model this method gives the exact values of the local magnetizations and the exact relation between equal-time and time-delayed correlations. It can also be used to solve efficiently the inverse problem, i.e. determine the couplings and local fields from a set of patterns, also in cases where the fields and couplings are time-dependent. This approach generalizes some recent attempts to solve this dynamical inference problem, which were valid in the limit of weak coupling. It provides the exact solution to the problem also in strongly coupled problems. This mean field inference can also be used as an efficient approximate method to infer the couplings and fields in problems which are not infinite range, for instance in diluted asymmetric spin glasses.Comment: 10 pages, 7 figure

Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence

This review reports on the research done during the past years on violations of the fluctuation-dissipation theorem (FDT) in glassy systems. It is focused on the existence of a quasi-fluctuation-dissipation theorem (QFDT) in glassy systems and the currently supporting knowledge gained from numerical simulation studies. It covers a broad range of non-stationary aging and stationary driven systems such as structural-glasses, spin-glasses, coarsening systems, ferromagnetic models at criticality, trap models, models with entropy barriers, kinetically constrained models, sheared systems and granular media. The review is divided into four main parts: 1) An introductory section explaining basic notions related to the existence of the FDT in equilibrium and its possible extension to the glassy regime (QFDT), 2) A description of the basic analytical tools and results derived in the framework of some exactly solvable models, 3) A detailed report of the current evidence in favour of the QFDT and 4) A brief digression on the experimental evidence in its favour. This review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the QFDT as well as for the more expert readers who may be interested in more specific results.Comment: 120 pages, 37 figures. Topical review paper . Several typos and misprints corrected, new references included and others updated. to be published in J. Phys. A (Math. Gen.