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

Abstract

In this paper, we studied chiral phase transitions in the Tsallis nonextensive statistics which has two parameters, the temperature [Formula: see text] and entropic parameter [Formula: see text]. 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 [Formula: see text] increases. The condensate at [Formula: see text] is smaller than that at [Formula: see text]. The sigma mass at [Formula: see text] is heavier than the mass at [Formula: see text] at high temperature, while the sigma mass at [Formula: see text] is lighter than the mass at [Formula: see text] at low temperature. The pion mass at [Formula: see text] is heavier than the mass at [Formula: see text]. The energy density increases remarkably as [Formula: see text] increases. The [Formula: see text] dependence in the case of the [Formula: see text]-expectation value is weaker than that in the case of the conventional expectation value with a Tsallis distribution. The parameter [Formula: see text] should be smaller than [Formula: see text] from energetic point of view. The validity of the Tsallis statistics can be determined by the difference in [Formula: see text] of the restriction for [Formula: see text] when the interaction is weak, because the parameter [Formula: see text] is smaller than [Formula: see text] in the case of the conventional expectation value with a Tsallis distribution.