# Lattice geometry and dispersion relation

Is there a general theorem which gives some information about which influence have the lattice geometry (for example sub-lattice structure, square lattice, honeycomb lattice, lattice symmetries, ...) to the dispersion relation in the low-energy regime?

For example: graphene or magnons in antiferromagnets. Both have a sub-lattice structure and the dispersion relations are linear.

The similarity between the linear dispersion in magnons and graphene may arise from the mathematical similarity in their formulation which comes from their sublattice structure, but it is a a lucky consequence of graphene also having electrons in the $2s^22p^2$ shells be mobile.