Summary and Conclusion

หัวข้อเรื่อง

	Summary and Conclusion
	To summarize, we have analyzed the vacancy-driven disordering process of an initially phase segregated binary system that is rapidly heated to a temperature T above criticality. To quantify the evolution of the system, we measure the number of broken bonds, A(L,t), as a function of time. This disorder parameter allows us to identify three temporal regimes, distinguished by the distribution of the vacancies through the system. The temporal growth of A during the latter regime is captured by the exponent ~ 0.5. If the final temperature is infinite, T=K , the motion of the vacancies is a simple Brownian random walk. For finite temperature T ³ 1.5T_c , we observe that these exponents still hold. Even though interparticle interactions now play an important role, correlations in the system are still short-range. And the vacancy is still a random walk by nature when the length scale exceeds the correlation length. As T approaches T_c, however, the correlation length reaches O(L), the simple random walk scenario breaks down. All the investigations above are focused on an up-quenches to the disordered state. A natural extension of this project is to set the final temperature below criticality. Needless to say, new questions and interesting phenomena can be expected. In particular, the final equilibrium state is still phase separated and all the interfacial properties come into play. With a single vacancy in a finite system, there may be a further separation of times scales. It is expected that soon after the early stage, the intrinsic density profile of the interface can be built. At this point, the interfacial width is most likely controlled by the correlation length . In the d=2 case, the interface is always rough, so that we can always expect the latter crossover to occur. We could study the equilibrium probability profile of the vacancy, i.e., where the vacancy spends most of its time. In case more than one vacancy are present, this profile should map into a density profile for the vacancies. In either case, it is expected that the vacancies will be trapped at the interface. Now, if more vacancies are added to system, the interface profile should be altered, since a preponderance of vacancies may significantly modify the interfacial energy. For d=3 Ising models, there are further interesting phenomena, associated with roughening transitions. Given that interfacial energies should depend on vacancy concentrations, how the locations (if not the nature) of such transitions are affected is a natural question. Finally, it would be extremely interesting to study the dynamic content of these systems, such as scaling properties when the up-quench is set at a roughening temperature. We conclude that even though our model is very simple, it forms the basis for the description of a large variety of related systems. Moreover, it is truly expected that considerable analytic progress is possible for a problem that is both nonlinear and time-dependent.