We present a study of the low-temperature phases of the antiferromagnetic extended classical Heisenberg model on the kagome lattice, up to third-nearest neighbors. First, we focus on the degenerate lines in the boundaries of the well-known staggered chiral phases. These boundaries have either semiextensive or extensive degeneracy, and we discuss the partial selection of states by thermal fluctuations. Then, we study the model under an external magnetic field on these lines and in the staggered chiral phases. We pay particular attention to the highly frustrated point, where the three exchange couplings are equal. We show that this point can be mapped to a model with spin-liquid behavior and nonzero chirality. Finally, we explore the effect of Dzyaloshinskii-Moriya (DM) interactions in two ways: a homogeneous and a staggered DM interaction. In both cases, there is a rich low-temperature phase diagram, with different spontaneously broken symmetries and nontrivial chiral phases.

中文翻译：

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Kagome格上扩展的Heisenberg模型中的简并手性态。

我们提出了反铁磁扩展经典海森堡模型在kagome晶格上直至第三近邻的低温相的研究。首先，我们着眼于众所周知的交错手性相边界中的简并线。这些边界具有半扩展或广泛的简并性，我们讨论了由热波动引起的状态的部分选择。然后，我们在这些线和交错的手性相的外部磁场下研究该模型。我们特别注意三个交换耦合相等的高度受挫点。我们证明了这一点可以映射到具有自旋液体行为和非零手性的模型。最后，我们以两种方式探讨Dzyaloshinskii-Moriya（DM）相互作用的影响：均质和交错DM相互作用。