Dipolar spin ice monopoles acquire finite magnetic charge from long-range dipole-dipole interactions via the dumbbell picture even classically, while octupolar spin ice monopoles have zero charge, providing a classical distinction between symmetry-enriched topological orders.
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Classical symmetry enriched topological orders and distinct monopole charges for dipole-octupole spin ices
Dipolar spin ice monopoles acquire finite magnetic charge from long-range dipole-dipole interactions via the dumbbell picture even classically, while octupolar spin ice monopoles have zero charge, providing a classical distinction between symmetry-enriched topological orders.