Effect of a lattice upon an interacting system of electrons: Breakdown of scaling and decay of persistent currents

For an interacting system of N electrons, we study the conditions under which a lattice model of size L with nearest neighbor hopping t and U/r Coulomb repulsion has the same ground state as a continuum model. For a fixed value of N, one gets identical results when the inter-electron spacing to the Bohr radius ratio r_s < r_s^*. Above r_s^*, the persistent current created by an enclosed flux begins to decay and r_s ceases to be the scaling parameter. Three criteria giving similar r_s^* are proposed and checked using square lattices.