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In this note we study a class of one-dimensional Ising chain having a highlydegenerated set of ground-state configurations. The model consists of spinchain having infinite-range pair interactions with a given structure. We showthat the set of ground-state configurations of such a model can be fullycharacterized by means of symbolic dynamics. Particularly we found that the setground- state configurations defines what in symbolic dynamics is called soficshift space. Finally we prove that this system has a non-vanishing residualentropy (the topological entropy of the shift space), which can be exactlycalculated.

Degenerated ground-states in a class of 1D Ising-like models: a characterization by symbolic dynamics