Antiferromagnetic model with known ground state

The ground state of the one-dimensional antiferromagnetic model, with the Hamiltonian H=1/2 j Sigma i=1n sigma i. sigma i+1+1/4j Sigma i=1n sigma i. sigma 1+2 n sigma i. sigma 1+2 (j>O, N even, N+1 identical to 1, N+2 identical to 2) can be given explicitly in terms of spin eigen-functions. Various properties of the ground state are studied. An approximate determination of the low-lying excited states shows the usual linear frequency-wave-vector relationship.