Dynamic Cavity Method in Fully-Asymmetric Models

Abstract

The physics of disordered systems is a broad and constantly evolving field. In this work, we focus on the study of discrete variable models with asymmetric interactions, in particular the fully-asymmetric ferromagnet and the fully-asymmetric Sherrington-Kirkpatrick. We use the cavity master equation, a well-known technique for the out-of-equilibrium dynamics, to derive average equations describing the time evolution of the magnetization and the energy in these models. In this way, we recovered previous results for the magnetization known from the literature and obtained new equations for the energy. With this work, we contribute to establish the cavity master equation as one of the most relevant techniques in the study of out-of-equilibrium systems and clarify its relationship with previous methods.