Chiral phase transitions in the linear sigma model in the Tsallis nonextensive statistics

Abstract

We studied chiral phase transitions in the Tsallis nonextensive statistics which has two parameters, the temperature $T$ and entropic parameter $q$. The linear sigma model was used in this study. The critical temperature, condensate, masses, and energy density were calculated under the massless free particle approximation. The critical temperature decreases as $q$ increases. The condensate at $q>1$ is smaller than that at $q=1$. The sigma mass at $q>1$ is heavier than the mass at $q=1$ at high temperature, while the sigma mass at $q>1$ is lighter than the mass at $q=1$ at low temperature. The pion mass at $q>1$ is heavier than the mass at $q=1$. The energy density increases remarkably as $q$ increases. The $q$ dependence in the case of the $q$-expectation value is weaker than that in the case of the conventional expectation value with a Tsallis distribution. The parameter $q$ should be smaller than $4/3$ from energetic point of view. The validity of the Tsallis statistics can be determined by the difference in $q$ of the restriction for $5/4<q<4/3$ when the interaction is weak, because the parameter $q$ is smaller than $5/4$ in the case of the conventional expectation value with a Tsallis distribution.

10 pages, 6 figures

References in corpus (7)

• Description of High-Energy pp Collisions Using Tsallis Thermodynamics: Transverse Momentum and Rapidity Distributions
• Modified Hagedorn formula including temperature fluctuation - Estimation of temperatures at RHIC experiments -
• Nonextensive effects on the relativistic nuclear equation of state
• Nonextensive effects in the Nambu--Jona-Lasinio model of QCD
• Nonextensive Nambu Jona-Lasinio model of QCD matter revisited
• Consistent nonadditive approach and nuclear equation of state
• Effects of Tsallis distribution on parametric resonance in chiral phase transitions

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• Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator
• Chiral phase transition in the linear sigma model within Hartree factorization in the Tsallis nonextensive statistics
• Relation between the escort average in microcanonical ensemble and the escort average in canonical ensemble in the Tsallis statistics
• Non-extensive Effects on the QCD Equation of State and Fluctuations of Conserved Charges within Polyakov Quark Meson Model