Vanishing Neel Ordering of SU(n) Heisenberg Model in Three Dimensions

The SU(n) Heisenberg model represented by exchange operators is studied by means of high-temperature series expansion in three dimensions, where n is an arbitrary positive integer. The spin-spin correlation function and its Fourier transform S(q) is derived up to O[(\beta J)^{10}] with (\beta J) being the nearest-neighbor antiferromagnetic exchange in units of temperature. The temperature dependence of S(q) and next-nearest-neighbor spin-spin correlation in the large n cases show that dominant correlation deviates from q=(\pi,\pi,\pi) at low temperature, which is qualitatively similar to that of this model in one dimension. The Neel temperature of SU(2) case is precisely estimated by analyzing the divergence of S(\pi,\pi,\pi). Then, we generalize n of SU(n) to a continuous variable and gradually increases from n=2. We conclude that the Neel ordering disappears for n>2.