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We discuss various aspects of the O(N)-model in the vacuum and at finitetemperature within the Phi-derivable expansion scheme to order lambda^2. Incontinuation to an earlier work, we look for a physical parametrization in theN=4 case that allows to accommodate the lightest mesons. Using zero-momentumcurvature masses to approximate the physical masses, we find that, in theparameter range where a relatively large sigma mass is obtained, the scale ofthe Landau pole is lower compared to that obtained in the two-loop truncation.This jeopardizes the insensitivity of the observables to the ultravioletregulator and could hinder the predictivity of the model. Both in the N=1 andN=4 cases, we also find that, when approaching the chiral limit, the(iterative) solution to the Phi-derivable equations is lost in an intervalaround the would-be transition temperature. In particular, it is not possibleto conclude at this order of truncation on the order of the transition in thechiral limit. Because the same issue could be present in other approaches, weinvestigate it thoroughly by considering a localized version of thePhi-derivable equations, whose solution displays the same qualitative features,but allows for a more analytical understanding of the problem. In particular,our analysis reveals the existence of unphysical branches of solutions whichcan coalesce with the physical one at some temperatures, with the effect ofopening up a gap in the admissible values for the condensate. Depending on itsrate of growth with the temperature, this gap can eventually engulf thephysical solution.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

The O(N)-model within the Phi-derivable expansion to order lambda^2: on  the existence, UV and IR sensitivity of the solutions to self-consistent  equations