Thermal-Cycle Memory Functions and Ising Dynamics

The Ising model provides a rich system for the study of a variety of correlated systems. In this talk, we present the results of numerical studies of 2- and 3-dimensional Ising spin systems subjected to thermal cycling from an ordered state to states with a fixed order parameter ($<$1), but with differing overall morphologies, and back to a quenched state. We find that for systems with initial states generated by thermal disordering above T$_{c}$, the initial state of a given order parameter has larger `islands' of like-spin (than the case for random disorder with the same overall order parameter) and consequent quenches of the state to T$<$T$_{c}$ result in a strong correlation to a particular final average order parameter. The function we find is given by $\left\langle S \right\rangle \approx \tanh (B\cdot S_{init} )$, where S$_{init}$ is the order parameter of the initial state, $<$S$>$ is the average quenched order parameter, and B is a constant that depends upon the morphology of the initial state. The reason for the strong correlation stems from the energies associated with spins at the borders of large clusters. This `memory effect' does not occur in 3D (due to the larger number of near-neighbors). Finally, we discuss the `memory function' in the context of interfacial states of liquid crystals.