Effects of the Tsallis distribution in the linear sigma model

TL;DR

This paper investigates how the Tsallis distribution, characterized by parameters q and T, influences physical quantities in the linear sigma model during chiral phase transitions, highlighting significant deviations from Boltzmann-Gibbs behavior.

Contribution

It introduces the application of the Tsallis distribution to the linear sigma model, analyzing its effects on phase transition properties and critical phenomena.

Findings

Chiral symmetry restoration occurs at lower temperatures for q>1.

Critical temperature decreases monotonically as q increases.

Small deviations from Boltzmann-Gibbs distribution cause large changes in physical quantities.

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.