Description of the paramagnet–spin glass transition in the Edwards–Anderson model using critical-dynamics methods

We show that the paramagnet–spin glass transition can be described in the Edwards–Anderson model using critical-dynamics methods and taking the ultrametric topology of the temporal space into account. In the framework of the suggested approach, we derive the Vogel–Fulcher relation for the system relaxation time. We prove that the fluctuation-dissipation theorem holds for the given model if there is no relaxation-time hierarchy.