Chiral Phase Transition at Finite Temperature in the Linear Sigma Model

Details Chiral Phase Transition at Finite Temperature in the Linear Sigma Model Chiral Phase Transition at Finite Temperature in the Linear Sigma Model

1996-11-26

arxiv.org/abs/nucl-th/9611050v1

Eur.Phys.J. A1 (1998) 205-220

Physics

Nuclear Physics

Nuclear Theory

21 pages, Latex

Scientific paper

10.1007/s100500050050

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.

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