We present a detailed study of the ground-state phase diagram of the classical frustrated Heisenberg model on the face-centered-cubic lattice. By considering exchange interactions to third nearest neighbors, we find commensurate, helimagnetic, as well as noncollinear, multi-Q orders which include noncoplanar and chiral spin structures. We reveal the presence of subextensively degenerate manifolds that appear at triple points and certain phase boundaries in the phase diagram. Within these manifolds, the spin Hamiltonian can be recast as a complete square of spins on finite motifs, permitting us to identify families of exact ground-state spin configurations in real space—these include randomly stacked ferro- or antiferromagnetically ordered planes and interacting ferromagnetic chains, among others. Finally, we critically investigate the ramifications of our findings on the example of the Ising model, where we exactly enumerate all the states numerically for finite clusters.

中文翻译：

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面心立方晶格上的经典海森堡反铁磁体中的简并流形，边形和多手性相

我们对面心立方晶格上的经典沮丧海森堡模型的基态相图进行了详细研究。通过考虑与第三近邻的交换相互作用，我们发现了相称的，日磁的以及非共线的多Q包括非共面和手性自旋结构的顺序。我们揭示了出现在相图中三重点和某些相界处的亚简并流形的存在。在这些流形中，自旋哈密顿量可以重铸成有限主题上的自旋的完整平方，从而使我们能够识别出真实空间中确切的基态自旋结构族，其中包括随机堆叠的铁磁或反铁磁有序平面以及相互作用的铁磁链等等。最后，我们以伊辛（Ising）模型为例，对发现的结果进行批判性研究，在该模型中，我们精确地枚举了有限簇的所有状态。