The polymer model framework is a classical tool from statistical mechanic . It has recently been used to obtain approximation algorithms for spin systemson classes of bounded-degree graphs . The edge perspective allows us to bound the growthrate of the number of polymers in terms of the total degree of the polymers, which in turn can be related more easily to the expansion properties of the underlying graph . We develop a less restrictive framework for polymer models that relaxes the standard bounded degree assumption, by reworking the relevant polymer modelsfrom the edge perspective . Our techniques also extend to more general spin systems . To apply our methods, we consider random graphs withunbounded degrees from a fixed degree sequence and obtain approximationalgorithms for the ferromagnetic Potts model, which is a standard benchmark forpolymer models. Our techniques include the ferrosmaic Potts models. We also obtain approximated algorithms for the Ferrosmagnetic Potts Model, which includes the ferroelectric Pottsmodel on expanders and on the grid and grid

Author(s) : Andreas Galanis, Leslie Ann Goldberg, James Stewart

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Keywords : degree - models - obtain - polymers - graphs -

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