We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ϕ4 theory in the ℤ2 symmetric phase. Already at NLO (one loop) the method is capable of generating a quite reasonable non-perturbative result for the critical coupling. At order-g7 we obtain gc = 2.779(25) which compares very well with the state of the art N8LO result, gc = 2.807(34). As a novelty we investigate the supercritical region showing that it contains some useful complimentary information that can be used in extrapolations to arbitrarily high orders.

We analyze the possible quantum phase transition patterns occurring within the O(N) × ℤ2 scalar multi-field model at vanishing temperatures in (1 + 1)-dimensions. The physical masses associated with the two coupled scalar sectors are evaluated using the loop approximation up to second order. We observe that in the strong coupling regime, the breaking O(N) × ℤ2→ O(N), which is allowed by the Mermin-Wagner-Hohenberg-Coleman theorem, can take place through a second-order phase transition. In order to satisfy this no-go theorem, the O(N) sector must have a finite mass gap for all coupling values, such that conformality is never attained, in opposition to what happens in the simpler ℤ2 version. Our evaluations also show that the sign of the interaction between the two different fields alters the transition pattern in a significant way. These results may be relevant to describe the quantum phase transitions taking place in cold linear systems with competing order parameters. At the same time the super-renormalizable model proposed here can turn out to be useful as a prototype to test resummation techniques as well as non-perturbative methods.

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