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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:math> and baryon chemical potential <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> in the framework of the linear sigma model. The corresponding nonextensive distribution, based on Tsallis’ statistics, is characterized by a dimensionless nonextensive parameter, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>, and the results in the usual Boltzmann-Gibbs case are recovered when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi>q</mml:mi><mml:mo>→</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:math>. The thermodynamics of the linear sigma model and its corresponding phase diagram are analysed. At high temperature region, the critical temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> is shown to decrease with increasing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math> from the phase diagram in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> plane. However, larger values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math> cause the rise of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> at low temperature but high chemical potential. Moreover, it is found that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M10"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math> different from zero corresponds to a first-order phase transition while <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M11"><mml:mi>μ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:math> to a crossover one. The critical endpoint (CEP) carries higher chemical potential but lower temperature with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M12"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math> increasing due to the nonextensive effects.

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