Encapsulated Spin Function for infinite lattices

An approximate spin function for infinite periodic spin lattices is introduced. The 〈 Encapsulated Spin Function 〉 is built from spin blocks variationally determined on open clusters. It gives a zeroth order description of the short range spin correlation while insuring a proper translational symmetry with an appropriate projection of the local spin function over the entire lattice. A recursion expression is derived that removes the normalization difficulty that arises in the projection. The one-dimensional Heisenberg regular hamiltonian is tested in the present report but the model allows for more complicated topologies of the interactions, including long range exchange and 3 spin exchange.