2022
DOI: 10.48550/arxiv.2211.04075
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Short-range and long-range order: a transition in block-gluing behavior in Hom shifts

Abstract: Hom shifts form a class of multidimensional shifts of finite type (SFT) and consist of colorings of the grid Z 2 where adjacent colours must be neighbors in a fixed finite undirected simple graph G. This class includes several important statistical physics models such as the hard square model. The gluing gap measures how far any two square patterns of size n can be glued, which can be seen as a measure of the range of order, and affects the possibility to compute the entropy (or free energy per site) of a shif… Show more

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