The chiral and deconfinement transitions: PNJL model beyond mean field

In Ref. [3] we have presented a way to calculate corrections beyond mean field, resolving issues related to the complex fermion determinant in the PNJL model. This is achieved by means of a perturbative approach establishing a systematically ordered series of correction terms. We define the unperturbed model by the Taylor expansion up to second order in the fields of the real part of the bosonized effective action of the NJL model1 plus the effective Polyakov loop potential2. The first term in such a Taylor expansion defines the mean field limit. Higher orders (beyond mean field) are treated using perturbative techniques. As a prominent example the thermal expectation values of the Polyakov loop 〈Φ〉 and its conjugate 〈Φ∗〉 are investigated here. Due to corrections beyond mean field the quantity 〈Φ〉−〈Φ∗〉 assumes non-vanishing values once