  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 version 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.
