To be specific, let's consider a finite lattice (in any dimension) with even number of sites, each containing a spin-1/2 interacting with other spin-1/2's via antiferromagnetic Heisenberg coupling. In such a setting, are there examples of systems which has non-spin singlet ground states?
It is known from Marshall's theorem that for a bipartite lattice (with equal size sublattices), the ground state is a global spin singlet.