Dynamical properties of a cluster model of spin-glasses

The dynamics of small decoupled Ising clusters with Gaussian-distributed interactions is examined. The exactly solved case of 4-spin clusters shows many dynamic properties of spinglasses. With a smoothly increasing cluster size the nonequilibrium susceptibility $\chi$ is in quantitative agreement with computer simulations of the Edwards-Anderson model of spin-glasses. A smooth change of the microscopic time constant gives a sharp peak in $\chi \mathrm{}\left(T\right)\mathrm{}$. Our results support the dynamical nature of the spin-glass transition.