Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

From the nonextensive statistical mechanics, we investigate the chiral phase transition at finite temperature T and baryon chemical potential μB in the framework of the linear sigma model. The corresponding nonextensive distribution, based on Tsallis’ statistics, is characterized by a dimensionless nonextensive parameter, q, and the results in the usual Boltzmann-Gibbs case are recovered when q→1. The thermodynamics of the linear sigma model and its corresponding phase diagram are analysed. At high temperature region, the critical temperature Tc is shown to decrease with increasing q from the phase diagram in the (T,μ) plane. However, larger values of q cause the rise of Tc at low temperature but high chemical potential. Moreover, it is found that μ different from zero corresponds to a first-order phase transition while μ=0 to a crossover one. The critical endpoint (CEP) carries higher chemical potential but lower temperature with q increasing due to the nonextensive effects.

Download Full-text

Chiral phase transition at finite temperature in the linear sigma model

The European Physical Journal A ◽

10.1007/s100500050050 ◽

1998 ◽

Vol 1 (2) ◽

pp. 205-220 ◽

Cited By ~ 26

Author(s):

Heui-Seol Roh ◽

T. Matsui

Keyword(s):

Phase Transition ◽

Finite Temperature ◽

Sigma Model ◽

Linear Sigma Model ◽

Chiral Phase ◽

Chiral Phase Transition

Download Full-text

Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator

International Journal of Modern Physics E ◽

10.1142/s0218301319500204 ◽

2019 ◽

Vol 28 (04) ◽

pp. 1950020 ◽

Cited By ~ 2

Author(s):

Masamichi Ishihara

Keyword(s):

Phase Transition ◽

Sigma Model ◽

Pion Mass ◽

Free Particle ◽

Chiral Condensate ◽

Linear Sigma Model ◽

Chiral Phase ◽

Chiral Phase Transition ◽

Nonextensive Statistics ◽

Particle Approximation

We studied the chiral phase transition for small [Formula: see text] within the Tsallis nonextensive statistics of the entropic parameter [Formula: see text], where the quantity [Formula: see text] is the measure of the deviation from the Boltzmann–Gibbs statistics. We adopted the normalized [Formula: see text]-expectation value in this study. We applied the free particle approximation and the massless approximation in the calculations of the expectation values. We estimated the critical physical temperature, and obtained the chiral condensate, the sigma mass, and the pion mass, as functions of the physical temperature [Formula: see text] for various [Formula: see text]. We found the following facts. The [Formula: see text]-dependence of the critical physical temperature is [Formula: see text]. The chiral condensate at [Formula: see text] is smaller than that at [Formula: see text] for [Formula: see text]. The [Formula: see text]-dependence of the pion mass and that of the sigma mass reflect the [Formula: see text]-dependence of the condensate. The pion mass at [Formula: see text] is heavier than that at [Formula: see text] for [Formula: see text]. The sigma mass at [Formula: see text] is heavier than that at [Formula: see text] for [Formula: see text] at high physical temperature, while the sigma mass at [Formula: see text] is lighter than that at [Formula: see text] for [Formula: see text] at low physical temperature. The quantities which are functions of the physical temperature [Formula: see text] and the entropic parameter [Formula: see text] are described by only the effective physical temperature defined as [Formula: see text] under the approximations.

Download Full-text