The ground state long range order has been studied for the isotropic quantum spin Hamiltonian with bilinear and biquadratic exchange interactions, J and J'. Through the estimation of infrared bound for the Fourier transformed spin correlation functions, the existence of the Neel long range order has been proved on the d dimensional hyper cubic lattices with arbitrary spin quantum number S(>=1). While some restricted conditions are assumed for the system, e.g. the uniqueness of the ground state etc., the proof is rigorus for J and J' satisfying all those conditions.
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