Oscillating propagators in heavy-dense QCD

Using Monte Carlo simulations and extended mean field theory calculations we show that the $3$-dimensional $\mathbb{Z}_3$ spin model with complex external fields has non-monotonic correlators in some regions of its parameter space. This model serves as a proxy for heavy-dense QCD in $(3+1)$ dimensions. Non-monotonic correlators are intrinsically related to a complex mass spectrum and a liquid-like (or crystalline) behavior. A liquid phase could have implications for heavy-ion experiments, where it could leave detectable signals in the spatial correlations of baryons.