Analytical and numerical approaches to the spin-facilitated kinetic Ising model

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Abstract
A survey is presented of recent progress in studying kinetically constrained Ising models using numerical approaches, a Fock-space formulation of the master equation and a mode-coupling approach, respectively. To this end, numerical results of various kinds are discussed, and also in connection with some ideas related to the glass transition. Furthermore, kinetically facilitated Ising models, considered as candidates for describing systems with a pronounced cooperativity, are reformulated in a second-quantized formulation. Using this approach, kinetic constraints can be incorporated into an analytical study. We discuss in great detail a one-dimensional model and mean-field approaches of several kinds; finally, we give some ideas for a mode-coupling approach to the slow dynamics of such kinetically constrained Ising models in higher dimensions.