A Bionic Coulomb Phase on the Pyrochlore Lattice

A class of three-dimensional classical lattice systems with macroscopic ground state degeneracies, most famously the spin ice system, are known to exhibit ``Coulomb'' phases wherein long wavelength correlations within the ground state manifold are described by an emergent Maxwell electrodynamics. We discuss a more elaborate example of this phenomenon---the four-state Potts model on the pyrochlore lattice---where the long wavelength description now involves three independent gauge fields, as we confirm via simulation. The excitations above the ground state manifold are bions, defects that are simultaneously charged under two of the three gauge fields, and they exhibit an entropic interaction dictated by these charges. We also show that the distribution of flux loops exhibits a scaling with loop length and system size previously identified as characteristic of Coulomb phases.