Strong Spatial Mixing and Rapid Mixing with Five Colours for the Kagome Lattice
نویسندگان
چکیده
منابع مشابه
Strong Spatial Mixing and Rapid Mixing with Five Colours for the Kagome Lattice
We consider proper 5-colourings of the kagome lattice. Proper q-colourings correspond to configurations in the zero-temperature q-state anti-ferromagnetic Potts model. Salas and Sokal have given a computer assisted proof of strong spatial mixing on the kagome lattice for q ≥ 6 under any temperature, including zero temperature. It is believed that there is strong spatial mixing for q ≥ 4. Here w...
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Recursively-constructed couplings have been used in the past for mixing on trees. We show how to extend this technique to non-tree-like graphs such as lattices. Using this method, we obtain the following general result. Suppose that G is a triangle-free graph and that for some Δ ≥ 3, the maximum degree of G is at most Δ. We show that the spin system consisting of q-colourings of G has strong sp...
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2009
ISSN: 1461-1570
DOI: 10.1112/s1461157000001492