On critical exponents without Feynman diagrams

2 00 1 Critical exponents predicted by grouping of Feynman diagrams in φ 4 model

Different perturbation theory treatments of the Ginzburg–Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The usual perturbation theory is reorganized by appropriate grouping of Feynman diagrams o...

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...

Multi-Particle Processes in QCD without Feynman Diagrams

A way to efficiently compute helicity amplitudes for arbitrary tree-level scattering processes in QCD is presented. The scattering amplitude is evaluated recursively through a set of Dyson-Schwinger equations. The computational cost of this algorithm grows asymptotically as 3n, where n is the number of particles involved in the process, compared to n! in the traditional Feynman graphs approach....

Multi-particle Processes in the Standard Model without Feynman Diagrams

A method to efficiently compute, in a automatic way, helicity amplitudes for arbitrary scattering processes at leading order in the Standard Model is presented. The scattering amplitude is evaluated recursively through a set of Dyson-Schwinger equations. The computational cost of this algorithm grows asymptotically as 3n, where n is the number of particles involved in the process, compared to n...

Feynman diagrams versus Fermi-gas Feynman emulator