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?
This isn't an area I'm very familiar with, but a quick google search turned up http://arxiv.org/abs/hep-lat/9509009. Looking at citations to it turns up a couple of handfuls of papers on a similar theme: http://inspirehep.net/search?ln=en&p=refersto:recid:399137 http://inspirehep.net/search?ln=en&p=refersto:recid:416261