Potts models on Feynman diagrams

Vertex Models on Feynman Diagrams

The statistical mechanics of spin models, such as the Ising or Potts models, on generic random graphs can be formulated economically by considering the N → 1 limit of N ×N Hermitian matrix models. In this paper we consider the N → 1 limit in complex matrix models, which describes vertex models of different sorts living on random graphs. From the graph theoretic perspective one is using matrix m...

Yang-Lee zeros of the two- and three-state Potts model defined on phi3 Feynman diagrams.

We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model...

Feynman diagrams versus Fermi-gas Feynman emulator

superstring Feynman diagrams

The multi-loop amplitudes for the closed, oriented superstring are represented by finite dimensional integrals of explicit functions calculated through the super-Schottky group parameters and interaction vertex coordinates on the supermanifold. The integration region is proposed to be consistent with the group of the local symmetries of the amplitude and with the unitarity equations. It is show...

Loops on Surfaces, Feynman Diagrams, and Trees

We relate the author’s Lie cobracket in the module additively generated by loops on a surface with the Connes-Kreimer Lie bracket in the module additively generated by trees.