  This paper is an extended erratum to J. Math. Phys.53, 042302 (2012) and
arXiv:1104.3443, in which the classic construction and Borel summability of the
phi^4_2 Euclidean quantum field theory was revisited combining a multi-scale
analysis with the constructive method called Loop Vertex Expansion (LVE).
Unfortunately we discovered an important error in the method of J. Math.
Phys.53, 042302 (2012). We explain the mistake, and provide a new, correct
construction of the phi^4_2 theory according to the LVE.
