Arithmetic of Potts model hypersurfaces

  title={Arithmetic of Potts model hypersurfaces},
  author={Matilde Marcolli and Jessica T. Su},
  journal={arXiv: Mathematical Physics},
We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition function). We focus on the behavior of the number of points over finite fields for these hypersurfaces, in comparison with the graph hypersurfaces of perturbative quantum field theory defined by the Kirchhoff graph polynomial. We give a very simple example of the failure of the "fibration condition" in the dependence of the Grothendieck class on the number of spin states and of… 

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