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

Abstract

We discuss various aspects of the O(N)-model in the vacuum and at finite temperature within the Phi-derivable expansion scheme to order lambda^2. In continuation to an earlier work, we look for a physical parametrization in the N=4 case that allows to accommodate the lightest mesons. Using zero-momentum curvature masses to approximate the physical masses, we find that, in the parameter range where a relatively large sigma mass is obtained, the scale of the Landau pole is lower compared to that obtained in the two-loop truncation. This jeopardizes the insensitivity of the observables to the ultraviolet regulator and could hinder the predictivity of the model. Both in the N=1 and N=4 cases, we also find that, when approaching the chiral limit, the (iterative) solution to the Phi-derivable equations is lost in an interval around the would-be transition temperature. In particular, it is not possible to conclude at this order of truncation on the order of the transition in the chiral limit. Because the same issue could be present in other approaches, we investigate it thoroughly by considering a localized version of the Phi-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 which can coalesce with the physical one at some temperatures, with the effect of opening up a gap in the admissible values for the condensate. Depending on its rate of growth with the temperature, this gap can eventually engulf the physical solution.

26 pages, 15 figures, uses RevTeX4-1, published version

References in corpus (4)

• Towards quantitative precision in the chiral crossover: masses and fluctuation scales
• Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase
• Renormalization of O(N) model in 1/N expansion in auxiliary field formalism
• Symmetry improvement of 3PI effective actions for O(N) scalar field theory

Cited by in corpus (17)

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• Symmetry-Improved 2PI Approach to the Goldstone-Boson IR Problem of the SM Effective Potential
• Functional renormalization group and 2PI effective action formalism
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• Localized rainbows in the QCD phase diagram
• One-loop constituent quark contributions to the vector and axial-vector meson curvature mass
• Axial anomaly and hadronic properties in a nuclear medium
• New algorithm to study the pseudo-Wigner solution of the quark gap equation in the framework of the (2+1)-flavor NJL model
• Padé approximants and analytic continuation of Euclidean Phi-derivable approximations
• Finite Temperature Description of an Interacting Bose Gas
• Loss of solution in the symmetry improved Phi-derivable expansion scheme
• Renormalization of the 4PI effective action using the functional renormalization group
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• Real effective potentials for phase transitions in models with extended scalar sectors
• The $O(4)$ ${\varphi }^4$ model as an effective light meson theory: A lattice-continuum comparison