Dense instanton-dyon liquid model: Diagrammatics

We revisit the instanton-dyon liquid model in the confined phase by using a nonlinear Debye-Huckel (DH) resummation for the Coulomb interactions induced by the moduli, followed by a cluster expansion. The organization is shown to rapidly converge and yields center symmetry at high density. The dependence of these results on a finite vacuum angle is also discussed. We also formulate the hypernetted chain (HNC) resummation for the dense instanton-dyon liquid and use it to estimate the liquid pair correlation functions in the DH limit. At very low temperature, the dense limit interpolates between chains and rings of instanton-anti-instanton dyons and a bcc crystal, with strong topological and magnetic correlations.