In 2D case we cannot neglect high-order terms in the expansion, because they have same canonical dimensions, therefore all terms are essential in the renormalization procedure (they are relevant). Thus, from that point of view the phi^4-approximation breaks down in 2D.
The question can't be answered as stated-it's incomplete. One answer is that, if one only keeps the phi^4 interaction term, one does find that this interaction does define a theory that's independent of the cutoff procedure used to describe it. One may ask, what happens, if one includes higher order terms. Cf. http://arxiv.org/abs/math-ph/0702077 or
https://projecteuclid.org/euclid.cmp/1103860122
for more precise statements. In particular the latter paper studies what's the effect of an external field that's not linear in phi and, thus, answers the question, what would happen, were another non-linear interaction included.
Stam, I have become familiar with the papers sent by you. Thank you!
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