Chiral phase transition from the Dyson-Schwinger equations in a finite spherical volume

Abstract: Within the framework of Dyson-Schwinger equations and by means of Multiple Reflection Expansion, we study the finite volume effects on the chiral phase transition in a sphere, especially discuss its influence on the location of the possible critical end point (CEP). According to our calculations, when we take the sphere instead of cube as a research, the influence of finite volume effects on phase transition is not as significant as previously calculated. For instance, as the radius of spherical volume decreases from infinite to $2 \mathrm{fm}$, at zero chemical potential and finite temperature, the critical temperature $T_{c}$ has only a slight drop. And at finite chemical potential and finite temperature, the location of CEP shifts toward smaller temperature and higher chemical potential, but the amplitude of variation does not exceed $20\%$. So we find that not only the size of the volume, but also the shape of the volume will have a considerable impact on the phase transition.