Close-packed structures with finite-range interaction: computational mechanics of layer pair interaction

The stacking problem is approached by computational mechanics, using an Ising next-nearest-neighbour model. Computational mechanics allows one 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. The occurrence of higher-order polytypes at the borders of the phase diagram is also analysed. The applicability of the model to real systems such as ZnS and cobalt is discussed. The method derived is directly generalizable to any one-dimensional model with finite-range interaction.