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

Abstract

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.

Small and Simple Systems That Favor the Arrow of Time

“…Computer simulations provide unique insight into how macroscopic behavior emerges from microscopic dynamics [15][16][17]. In fact, the first molecular dynamics (MD) simulations on a digital computer surprised Enrico Fermi and his team by showing that small anharmonic systems governed by Newton's laws fail to reach thermal equilibrium [18].…”