Chiral phase transition in linear sigma model with non-extensive statistical mechanics

From the non-extensive statistical mechanics, we investigate the chiral phase transition at finite temperature $T$ and baryon chemical potential $\mu_B$ in the framework of the linear sigma model. The corresponding non-extensive distribution, based on Tsallis' statistics, is characterized by a dimensionless non-extensive parameter, $q$, and the results in the usual Boltzmann-Gibbs case are recovered when $q\to 1$. The thermodynamics of the linear sigma model and its correspodning phase diagram are analysed. At high temperature region, the critical temperature $T_c$ is shown to decrease with increasing $q$ from the phase diagram in the $(T,~\mu)$ plane. However, larger values of $q$ causes the rise of $T_c$ at low temperature but high chemical potential. Moreover, it is found that $\mu$ different from zero corresponds to a first-order phase transition while $\mu=0$ to a crossover one. The critical endpoint (CEP) carries higher chemical potential but lower temperature with $q$ increasing due to the non-extensive effects.