Effects of the Tsallis distribution in the linear sigma model

Abstract

The effects of the Tsallis distribution which has two parameters, $q$ and $T$,on physical quantities are studied using the linear sigma model in chiral phase transitions. The Tsallis distribution approaches the Boltzmann-Gibbs distribution as $q$ approaches $1$. The parameter $T$ dependences of the condensate and mass for various $q$ are shown, where $T$ is called temperature. The critical temperature and energy density are described with digamma function, and the $q$ dependences of these quantities and the extension of Stefan-Boltzmann limit of the energy density are shown. The following facts are clarified. The chiral symmetry restoration at $q>1$ occurs at low temperature, compared with the restoration at $q=1$.The sigma mass and pion mass reflect the restoration. The critical temperature decreases monotonically as $q$ increases. The small deviation from the Boltzmann-Gibbs distribution results in the large deviations of physical quantities, especially the energy density. It is displayed from the energetic point of view that the small deviation from the Boltzmann-Gibbs distribution is realized for $q>1$. The physical quantities are affected by the Tsallis distribution even when $|q-1|$ is small.

11 pages, 6figures; some parts were modified

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Cited by in corpus (13)

• Analytic results for the Tsallis thermodynamic variables
• Phase transition for the system of small volume in the ${\varphi }^4$ theory in the Tsallis nonextensive statistics
• Effects of the Tsallis distribution in the linear sigma model
• Chiral phase transitions in the linear sigma model in the Tsallis nonextensive statistics
• Momentum distribution and correlation for a free scalar field in the Tsallis nonextensive statistics based on density operator
• Transverse momentum fluctuation under the Tsallis distribution at high energies
• Momentum Distribution and Correlation due to mass difference caused by power-like distribution
• Chiral phase transition in the linear sigma model within Hartree factorization in the Tsallis nonextensive statistics
• Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator
• Bounds on the Tsallis Parameter from a deformed Neutrino Sector in the Early Universe
• Relation between the escort average in microcanonical ensemble and the escort average in canonical ensemble in the Tsallis statistics
• Effects of Tsallis distribution on parametric resonance in chiral phase transitions
• Non-extensive Effects on the QCD Equation of State and Fluctuations of Conserved Charges within Polyakov Quark Meson Model