Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2011-04-18
Nucl.Phys.B853:688--709,2011
Physics
High Energy Physics
High Energy Physics - Lattice
15 pages RevTeX, 9 figures; v2: matches published version, some clarifying remarks added, discussion of the applicability of t
Scientific paper
10.1016/j.nuclphysb.2011.08.010
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.
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