| This work investigates the early time behavior of systems in which the temperature is lowered from above to below the critical temperature. Such systems can evolve to their equilibrium state along several paths. One such path is the process of ordering, in which a material changes from one structure to another. This work presents the results of comparisons between Monte Carlo simulations of systems which undergo the process of ordering and a theory developed by Cahn, Hilliard and Cook (CHC), which should describe the early stages of this process.;To perform this comparison, I estimated the correlation function of a ferromagnetic model using Monte Carlo simulations and then fit this correlation function to the forms predicted by the CHC theory. Results of this comparison show that CHC theory fails to describe the early time evolution of the system at length scales on the order of the correlation length and smaller, a regime where the theory is expected to work. An alternative linear theory is proposed here which accounts for evolution on length scales on the order of the correlation length, though it also fails at smaller length scales.;It is further shown that the failure of the proposed linear theory manifests itself as domains which develop as the system evolves. Using a cluster mapping developed by Coniglio and Klein, it is possible to identify domains of enhanced magnetization which form early in the evolution of the system. These domains have a large magnetization and distinct boundaries which indicates that their formation and growth are not governed by any linear theory even at earliest times. Initially these domains are isolated and grow independently. As they grow, the domains begin to interact at a time which corresponds to the characteristic time at which the linear theory fails completely. The conclusion of this work is that the interior of these structures cannot be described by a linear theory, and that the linear theory fails to describe any length scale of the system after these structures start to coalesce. |
