Abstract
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in equilibrium with a thermal bath. We propose a fluctuation principle that allows us to derive fluctuation–dissipation relations for many-time correlations and linear responses. We also speculate on how these features will be modified in systems evolving slowly out of equilibrium, such as finite-dimensional or dilute spin-glasses. Secondly, we present a formalism that allows one to derive a series of approximated equations that determine the dynamics of disordered spin models on random (hyper) graphs.
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