Lattice Simulations on a Sphere in Condensed Matter

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Most lattices I've come across in condensed matter, like the Kitaev model, are regular lattices and don't fit on a sphere.

Are lattice simulations ever put on a sphere in condensed matter, and if so what sort of lattice is used?
 
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Hi. I have got question as in title. How can idea of instantaneous dipole moment for atoms like, for example hydrogen be consistent with idea of orbitals? At my level of knowledge London dispersion forces are derived taking into account Bohr model of atom. But we know today that this model is not correct. If it would be correct I understand that at each time electron is at some point at radius at some angle and there is dipole moment at this time from nucleus to electron at orbit. But how...

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