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The Ising model doesn't have a strictly defined dynamics, only a spectrum.There are different ways to equip it with a time dependence e.g. the Glauber orthe Kawasaki dynamics, which are both stochastic, but it means there is amaster equation which can also describes their dynamics. We present aGluber-type master equation derived from the Redfield equation, where the spinsystem is coupled to a bosonic bath. We derive a time dependent mean fieldequation which describes the relaxation of the spin system at finitetemperature. Using the fully connected, uniform Ising model the relaxation timewill be studied, and the critical behaviour around the critical temperature.The master equation shows the finite size effects, and the mean field equationthe thermodynamic limit.

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