Zhaoxi Xiong, Xiao-Gang Wen
We present a general method for systematically finding the families of exact ground states of classical Heisenberg models with the following properties: (${i}$) they have the translational symmetries of infinite crystals; and (${ii}$) they contain only bilinear terms, i.e. $\vec S_i \cdot \vec S_j$. With very limited exceptions, the method is applicable to all such models with one spin per unit cell, and models that have many spins per unit cell and satisfy certain conditions. Crystal dimensionality, range of coupling, etc. do not affect the validity. We also prove theorems that guarantee the existence of, in certain circumstances, a spiral state within the ground state manifold. Our formalism is predictive for disorder, and it might be generalized to higher-order terms (i.e. $(\vec S_i \cdot \vec S_j)^r$), anisotropic couplings, and arbitrary dimensional spins.
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http://arxiv.org/abs/1208.1512
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