Fluctuation induced first order phase transition in U(n)xU(n) models using chiral invariant expansion of functional renormalization group flows

Phase transition in U(n)xU(n) models is investigated for arbitrary flavor number n. We present a nonperturbative, 3+1 dimensional finite temperature treatment of obtaining the effective potential, based on a chiral invariant expansion of the functional renormalization group flows. The obtained tower of equations is similar but not identical to that of the Dyson-Schwinger hierarchy and has to be truncated for practical purposes. We investigate the finite temperature behavior of the system in an expansive set of the parameter space for n = 2, 3, 4 and also perform a large-n analysis. Our method is capable of recovering the one-loop beta functions of the coupling constants of the epsilon expansion; furthermore, it shows direct evidence that regardless of the actual flavor number, within our approximation, the system undergoes a fluctuation induced first order phase transition.Comment: 12 pages, 6 figures, typos corrected, Version published in Phys. Rev.

Functional dependence of axial anomaly via mesonic fluctuations in the three flavor linear sigma model

Temperature dependence of the $U_A(1)$ anomaly is investigated by taking into account mesonic fluctuations in the $U(3)\times U(3)$ linear sigma model. A field dependent anomaly coefficient function of the effective potential is calculated within the finite temperature functional renormalization group approach. The applied approximation scheme is a generalization of the chiral invariant expansion technique developed in [G. Fejos, Phys. Rev. D 90, 096011 (2014)]. We provide an analytic expression and also numerical evidence that depending on the relationship between the two quartic couplings, mesonic fluctuations can either strengthen of weaken the anomaly as a function of the temperature. The role of the six-point invariant of the $U(3)\times U(3)$ group, and therefore the stability of the chiral expansion is also discussed in detail.Comment: 10 pages, 3 figures, minor changes, Published in Phys. Rev.

Thermal properties and evolution of the UA(1)U_A(1) factor for 2+1 flavors

Thermal evolution of the axial anomaly is investigated in the system of the linear sigma model for $2+1$ flavors. We explore the functional form of the effective potential and the coefficient of the `t Hooft determinant term. It is found that the latter develops a non-trivial structure as a function of the chiral condensate and grows everywhere with respect to the temperature. This shows that mesonic fluctuations strengthen the axial anomaly at finite temperature and it does not get vanished at the critical point. The phenomenon has been found to have significance in the thermal properties of the mesonic spectra, especially concerning the $\eta-\eta'$ system.Comment: 9 pages, 6 figures, typos corrected, matches published versio

Spontaneously broken ground states of the U(n)_L x U(n)_R linear sigma model at large n

Symmetry breaking patterns of the U(n)_L x U(n)_R symmetric meson model are investigated in a formulation involving three auxiliary composite fields. The effective potential is constructed at leading order in the 1/n expansion for a condensate belonging to the center of the U(n) group. A wide region is found in the coupling space where in addition to the condensate proportional to the unit matrix, also metastable minima exist, in which a further breakdown of the diagonal U_V(n) symmetry to U_V(n-1) is realized. Application of a moderate external field conjugate to this component of the order parameter changes this state into the true ground state of the system.Comment: ReVTeX4, 10 pages, 5 figures. Extended introduction and conclusion. Version published in Phys. Rev.

Renormalized O(N) model at next-to-leading order of the 1/N expansion: Effects of the Landau pole

Apparently convergent contributions of resummed perturbative series at the next-to-leading order of the 1/N expansion in the O(N) model are reanalyzed in terms of renormalizability. Compared to our earlier article [G. Fejos et al., Phys. Rev. D 80, 025015 (2009)], an additional subtraction is performed. We show numerically that this is indispensable for diminishing the cutoff sensitivity of some integrals below the scale of the Landau pole. Following the method of our earlier article, an improved counterterm Lagrangian is constructed in the two-particle irreducible formalism, with and without the use of an auxiliary field formulation.Comment: 12 pages, 2 figures. Version published in Phys. Rev.