ARITHMETIC OF POTTS MODEL HYPERSURFACES

DOI10.1142/S0219887813500059zbMath1266.82017arXiv1112.5667OpenAlexW2963506046MaRDI QIDQ4917807

Jessica Su, Matilde Marcolli

Publication date: 2 May 2013

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.5667

zbMATH Keywords

zeta functionPotts modelsmixed Tate motivespoints over finite fields

Mathematics Subject Classification ID

Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Varieties over finite and local fields (11G25)

Related Items (1)

Potts models with magnetic field: arithmetic, geometry, and computation

Cites Work

• Cohomology of graph hypersurfaces associated to certain Feynman graphs
• Parametric Feynman integrals and determinant hypersurfaces
• On motives associated to graph polynomials
• Quantum periods: a census of \(\phi^4\)-transcendentals
• Mixed Hodge structures and renormalization in physics
• Feynman motives of banana graphs
• Zero-free regions for multivariate tutte polynomials (alias Potts-model partition functions) of graphs and matroids
• Spanning trees and a conjecture of Kontsevich
• Counting points on varieties over finite fields related to a conjecture of Kontsevich
• The Galois coaction on the electron anomalous magnetic moment
• A motivic approach to phase transitions in Potts models
• Graph hypersurfaces and a dichotomy in the Grothendieck ring
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Monte-Carlo approximation algorithms for enumeration problems
• On the computational complexity of the Jones and Tutte polynomials
• The universal Euler characteristic for varieties of characteristic zero
• The massless higher-loop two-point function

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