Chiral phase transition at finite temperature in the linear sigma model

Abstract

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength.

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

“…We clearly see a first order phase transition around T c = 200MeV. This agrees with other mean field approaches [15,16,5]. The renormalisation group however, leads us to believe that the actual phase transition of the 13 O(4) linear sigma model should be second order.…”

“…This model has always been a fertile ground to test ideas and check approximations in finite temperature quantum field theory [3] and has recently attracted renewed interest [4][5][6][7][8][9][10][11] because of its relevance to the thermodynamics of chiral symmetry in Q.C.D. Many treatments of finite T O(N) linear σ-model use the Hartree approximation which sums bubble graphs (daisy and superdaisy graphs).…”

Thermalization in a Hartree ensemble approximation to quantum field dynamics

“…4 we discuss vacuum and thermal stationary state solutions. We note one of the flaws of the Hartree approximation, the fact that it predicts a first order phase transition where there should only be a cross-over (in 3+1 D one also gets a first order transition [21] instead of the expected second order; the inconsistency problem with coupling constant renormalization [21] is absent in 1+1 dimensions). Numerical results for the evolution from initial out-of-equilibrium distributions are presented in Sec.…”

Thermodynamics ofO(N)sigma models:1/Ncorrections

“…In the low-temperature phase, the O(N ) symmetry is spontaneously broken and it is expected that the symmetry is restored via a secondorder phase transition. The calculations of the effective potential as a function of temperature have been carried out in the Hartree approximation and the large-N limit [10,11,12,13,14,15]. In these cases, the gap equations for the propagators are easy to solve since the self-energy reduces to a local mass term.…”