Brazovskii–Dyugaev effect on the inhomogeneous chiral transition in quark matter

We investigate the effects of quantum and thermal fluctuations on the phase boundary between the inhomogeneous chiral phase and the chiral-restored phase in the phase diagram in the plane of temperature and chemical potential. Introducing the composite fields made of quark bilinear fields, we construct an effective action for them in quark matter by way of the correlation function method. Utilizing this effective action, we discuss the effects of the quark–antiquark and particle–hole pair fluctuations to find possible modifications of the vertex functions of the order parameter included in the thermodynamic potential. We find that the most important effect of the pair fluctuations is to change the sign of the fourth-order vertex function to make the phase transition always the first, rather than the second, order (we call it the Brazovskii–Dyugaev effect). Another important effect manifests in the second-order vertex function: it exhibits a singular behavior near the critical point, which prohibits the second-order phase transition. It, together with the fourth-order vertex function, alters the location of the phase boundary.