A method for resummation of perturbative series based on the stochastic solution of Schwinger-Dyson equations

Abstract

We propose a numerical method for resummation of perturbative series, which is based on the stochastic perturbative solution of Schwinger-Dyson equations. The method stochastically estimates the coefficients of perturbative series, and incorporates Borel resummation in a natural way. Similarly to the "worm" algorithm, the method samples open Feynman diagrams, but with an arbitrary number of external legs. As a test of our numerical algorithm, we study the scale dependence of the renormalized coupling constant in a theory of one-component scalar field with quartic interaction. We confirm the triviality of this theory in four and five space-time dimensions, and the instability of the trivial fixed point in three dimensions.

15 pages RevTeX, 9 figures; v2: matches published version, some clarifying remarks added, discussion of the applicability of the method to non-Abelian gauge theories extended

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• Bold Diagrammatic Monte Carlo Study of ${\varphi }^4$ Theory
• Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model
• Full and unbiased solution of the Dyson-Schwinger equation in the functional integro-differential representation
• Monte Carlo Computation of Spectral Density Function in Real-Time Scalar Field Theory
• Metropolis updates for Diagrammatic Monte-Carlo algorithms from Schwinger-Dyson equations
• Feasibility of Diagrammatic Monte-Carlo based on weak-coupling expansion in asymptotically free theories: case study of $O(N)$ sigma-model in the large-$N$ limit