Dynamics of Ising models coupled microscopically to bath systems

TL;DR

This paper investigates the nonlinear dynamics of Ising models coupled to baths using two approaches: a master equation with microscopically derived transition rates and coupled equations for magnetizations and energy, applied to spin glasses.

Contribution

It introduces two complementary methods for analyzing Ising systems coupled to baths, including microscopically founded transition rates and coupled equations of motion.

Findings

Derived transition rates differ from phenomenological ones.

Applied methods to the Sherrington-Kirkpatrick spin glass model.

Provided simple examples illustrating the approaches.

Abstract

Based on the Robertson theory the nonlinear dynamics of general Ising systems coupled microscopically to bath systems is investigated leading to two complimentary approaches. Within the master equation approach microscopically founded transition rates are presented which essentially differ from the usual phenological rates. The second approach leads to coupled equations of motion for the local magnetizations and the exchange energy. Simple examples are discussed and the general results are applied to the Sherrington-Kirkpatrick spin glass model.