Arithmetic of Potts model hypersurfaces

Details Arithmetic of Potts model hypersurfaces Arithmetic of Potts model hypersurfaces

2011-12-23

arxiv.org/abs/1112.5667v1

Physics

Mathematical Physics

19 pages, latex, 2 pdf figures

Scientific paper

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 the polynomial countability condition for these Potts model hypersurfaces. We then show that a period computation, formally similar to the parametric Feynman integrals of quantum field theory, arises by considering certain thermodynamic averages. One can show that these evaluate to combinations of multiple zeta values for Potts models on polygon polymer chains, while silicate tetrahedral chains provide a candidate for a possible occurrence of non-mixed Tate periods.

Affiliated with

Also associated with

No associations

Rating

Arithmetic of Potts model hypersurfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Arithmetic of Potts model hypersurfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Arithmetic of Potts model hypersurfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-590498