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The Coulomb phase in frustrated systems


In this talk, I review the "Coulomb phase", an emergent state of various 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 consequence:

(1) correlation functions have the same functional form as a dipole-dipole interaction, meaning they are (surprisingly) long-ranged; correspondingly, in reciprocal space, the (all diffuse) scattering has characteristic  "pinch-point" singularities

(2) topological defects (where the local constraint is violated) behave like effective charges with Coulomb interactions.

Time permitting, I will mention extensions and applications of the Coulomb phase idea to (a) dynamics, (b) quantum mechanics,  (c) phase transitions out of such states, and/or (d) models with disorder.