Abstract

We describe a numerical method for resummation of perturbative expansions in quantum field theories, which is based on the stochastic solution of Schwinger-Dyson equations. Our algorithm randomly generates open Feynman diagrams with probability proportional to their weight times some factor which compensates the combinatorial growth of their number. Perturbative series can be then easily re-summed by a Pade-Borel-Leroy procedure. As a simple test of our method, we apply it to a theory of one-component scalar field with quartic interaction. Resummation of perturbative expansion of renormalized coupling constant confirms that this theory is trivial in four and five space-time dimensions, and that the trivial fixed point is unstable in three dimensions.

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