The 2PI finite temperature effective potential of the O(N) linear sigma model in 1+1 dimensions, at next-to-leading order in 1/N

Abstract

We study the O(N) linear sigma model in 1+1 dimensions. We use the 2PI formalism of Cornwall, Jackiw and Tomboulis in order to evaluate the effective potential at finite temperature. At next-to-leading order in a 1/N expansion one has to include the sums over "necklace" and generalized "sunset" diagrams. We find that - in contrast to the Hartree approximation - there is no spontaneous symmetry breaking in this approximation, as to be expected for the exact theory. The effective potential becomes convex throughout for all parameter sets which include N=4,10,100, couplings lambda=0.1 and 0.5, and temperatures between 0.2 and 1. The Green's functions obtained by solving the Schwinger-Dyson equations are enhanced in the infrared region. We also compare the effective potential as function of the external field phi with those obtained in various other approximations.

19 pages, 9 figures; v2: references added, some changes in the text

References in corpus (8)

• Renormalization of Φ-derivable approximations in scalar field theories
• Shear Viscosity in the O(N) Model
• Quantum dynamics of phase transitions in broken symmetry $\lambda {\varphi }^4$ field theory
• Transport coefficients from the 2PI effective action
• The O(N) linear sigma model at finite temperature beyond the Hartree approximation
• Kinks in the Hartree approximation
• Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism
• Quantum dynamics of Phi**4 field theory beyond leading order in 1+1 dimensions

Cited by in corpus (6)

• Nonperturbative resummation of de Sitter infrared logarithms in the large-N limit
• Functional renormalization group and 2PI effective action formalism
• 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
• Counterterm resummation for 2PI-approximation in constant background
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• One-meson-loop NJL model: Effect of collective and noncollective excitations on the quark condensate at finite temperature