Multiscale Loop Vertex Expansion for Cumulants, the ${\varphi }_2^4$ Model

Abstract

We consider the ${\varphi }_2^4$ model. It has been called the simplest non- trivial super-renormalisable model. The method we use is the multiscale loop vertex expansion, an improvement of constructive field theory. We prove analyticity and Borel summability of the cumulants up to a finite order.

30 pages, 5 figures