  A quantum anti-ferromagnetic spin-1 model is characterised on a 2D lattice
with the following requirements: i) The Hamiltonian is made out of nearest
neighbour interactions. ii) It is homogeneous, translational and rotational
invariant. iii) The ground state is a real singlet state of SU(2) (non-chiral).
iv) It has a local spin-1 representation. Along the way to characterise the
system, connections with classical statistical mechanics and integrable models
are explored. Finally, the relevance of the model in the physics of low
dimensional anti-ferromagnetic Mott-Hubbard insulators is discussed.
