Computational mechanics of Ising models of close packed structures

What is it about?

The stacking problem is approached by computational mechanics, using an Ising next nearest neighbor model. Computational mechanics allows to treat the stacking arrangement as an information processing system in the light of a symbol generating process. A general method for solving the stochastic matrix of the random Gibbs field is presented, and then applied to the problem at hand. The corresponding phase diagram is then discussed in terms of the underlying epsilon-machine, or optimal finite state machine, describing statistically the system. The occurrence of higher order polytypes at the borders of the phase diagram is also analyzed. Discussion of the applicability of the model to real system such as ZnS and Cobalt is done. The method derived is directly generalizable to any one dimensional model with finite range interaction.

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Why is it important?

With the development of computational mechanics by Prof. Crutchfield and coworkers, its importance as a tool for studying polytipism has been proven in a number of contexts. Yet, in spite of being one of its earlier applications, the approach of Computational Mechanics to Ising model has not been applied to polytipism. Thermodynamic models of polytypism have a long history, specially those concerning the use of Ising type model. Revisiting such models under the perspective of Computational Mechanics is the goal of this contribution. We intende to show that such approach is valuable for a number of reasons, of which we would like to emphasize: 1) It allows a thorough discussion of the appearance of stable and metastable polytipic phases in a natural way, which is much more involved with other approaches. 2) A discussion of disorder in polytipic phases an their corresponding phase transitions can be followed within a unique framework which, additionally, uses entropic magnitudes such as entropy density and excess entropy as quantitative measure of disorder and structure. Such analysis is not found in previous analysis. 3) It allows the analysis also of the origins of polytypism in solids, an opens new venues into the understanding of an old problem.