Study of the O(N) linear $\sigma$ model at finite temperature using the 2PPI expansion

Abstract

We show that a new expansion which sums seagull and bubble graphs to all orders, can be applied to the O(N)-linear σ-model at finite temperature. We prove that this expansion can be renormalised with the usual counterterms in a mass independent scheme and that Goldstone's theorem is satisfied at each order. At the one loop order of this expansion, the Hartree result for the effective potential (daisy and superdaisy graphs) is recovered. We show that at one loop 2PPI order, the self energy of the σ-meson can be calculated exactly and that diagrams are summed beyond the Hartree approximation.

Mass gap and vacuum energy of the Gross-Neveu model via the 2-point-particle-irreducible expansion

“…In this paper, we address another approach, the socalled 2P P I expansion. Its first appearance and use for analytical finite temperature research can be found in [8,9,10,11,12]. In Sec.II, we give a new derivation of the expansion.…”

Erratum: False vacuum decay by self-consistent bounces in four dimensions [Phys. Rev. D75, 045001 (2007)]

“…With the present choice of the finite renormalizations we have .27) and 29) and the condition U ′ eff (φ tv ) = 0 leads to…”

“…The other finite parts have been set to zero. For the renormalization of the Hartree back-reaction it is essential that for a mass-independent regularization scheme all divergent parts are related [22,29]. As a consequence these divergences can be conveniently removed by one counter term [30] Fixing the remaining counter terms becomes more involved; due to the nonlinearity of the gap equation we get a set of nonlinear equations.…”

Two-particle irreducible finite temperature effective potential of theO(N)linear sigma model in1+1dimensions at next-to-leading order ofBaacke1, Michalski2 2004Phys. Rev. D

“…It is usually motivated by a self-consistency of one-loop quantum corrections. It has been studied in 3 + 1 dimensions by various authors, in thermal equilibrium [8,9,10,11,12], and out-of-equilibrium [13]. The model with spontaneous symmetry breaking is found to have a phase transition of first order towards the symmetric phase at high temperature.…”