Chiral phase transition at finite temperature
in the linear sigma model
Heui-Seol Roh - T. Matsui
Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606, Japan
Recieved: 19 September 1997 / Revised version: 30 October 1997 Communicated by F. Lenz
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.
PACS
25.75.-q Relativistic heavy-ion collisions -
11.30.Rd Chiral symmetries -
12.39.-x Phenomenological quark models
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