Software for mean field calculations with fermions on a lattice

I know there is lots of software for practical calculations with DFT method, but I am more interested in toy models here. Is there any software for calculating mean-field phase transitions for interacting fermions on a lattice? Something, where one could set-up a toy model with interacting electrons and get mean-field predictions for antiferromagnetic/superconducting/charge-density-wave transition temperatures or other parameters.