Chiral Phase Transition in Linear Sigma Model with Nonextensive Statistical Mechanics

From the nonextensive statistical mechanics, we investigate the chiral phase transition at finite temperature and baryon chemical potential in the framework of the linear sigma model. The corresponding nonextensive distribution, based on Tsallis’ statistics, is characterized by a dimensionless nonextensive parameter, , and the results in the usual Boltzmann-Gibbs case are recovered when . The thermodynamics of the linear sigma model and its corresponding phase diagram are analysed. At high temperature region, the critical temperature is shown to decrease with increasing from the phase diagram in the plane. However, larger values of cause the rise of at low temperature but high chemical potential. Moreover, it is found that different from zero corresponds to a first-order phase transition while to a crossover one. The critical endpoint (CEP) carries higher chemical potential but lower temperature with increasing due to the nonextensive effects.