The Coulomb Phase in Frustrated Systems

The Coulomb phase is an emergent state for lattice models (particularly highly frustrated antiferromagnets), which have local constraints that can be mapped to a divergence-free flux. The coarse-grained versions of this flux or polarization behave analogously to electric or magnetic fields; in particular, defects at which the local constraint is violated behave as effective charges with Coulomb interactions. I survey the derivation of the characteristic power-law correlation functions and the pinch points in reciprocal space plots of diffuse scattering, as well as applications to magnetic relaxation, quantum-mechanical generalizations, phase transitions to long-range-ordered states, and the effects of disorder.