Relaxation of the Ising spin system coupled to a bosonic bath and the time dependent mean field equation

The Ising model does not have strictly defined dynamics, only a spectrum. There are different ways to equip it with time dependence, e.g., the Glauber or the Kawasaki dynamics, which are both stochastic, but it means there is a master equation that can also describe their dynamics. These equations can be derived from the Redfield equation, where the spin system is weakly coupled to a bosonic bath. In this paper, we investigate the temperature dependence of the relaxation time of a Glauber-type master equation, especially in the case of the fully connected, uniform Ising model. The finite-size effects were analyzed with a reduced master equation and the thermodynamic limit with a time-dependent mean field equation.

Automated summary

The Ising model, which lacks strictly defined dynamics, can be equipped with time dependence through methods such as the Glauber or Kawasaki dynamics. This paper focuses on investigating the temperature dependence of the relaxation time in a Glauber-type master equation, specifically in the case of the fully connected and uniform Ising model. Finite-size effects are analyzed using a reduced master equation, while the thermodynamic limit is examined with a time-dependent mean field equation.