  Using Monte Carlo simulations and extended mean field theory calculations we
show that the $3$-dimensional $Z_3$ spin model with complex external fields has
non-monotonic spatial correlators in some regions of its parameter space. This
model serves as a proxy for heavy-dense QCD in $(3+1)$ dimensions.
Non-monotonic spatial 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.
