  In this paper we construct the 2 dimensional Euclidean $\phi^4$ quantum field
theory using the method of loop vertex expansion. We reproduce the results of
standard constructive theory, for example the Borel summability of the
Schwinger functions in the coupling constant. Our method should be also
suitable for the future construction of Grosse-Wulkenhaar models on
non-commutative space-time.
