半球形水冰$I_h$中的极化平台
Polarization Plateaus in Hexagonal Water Ice $I_h$
摘要：
水冰中的质子受到所谓的\emph{ice rules}的影响，导致广泛的基态简并。我们研究了如何在一个极小模型内的外部电场减少这种基态简并在六角形水冰I $_h$。我们观察到偏振平台时，字段是沿着$[001]$和$[010]$方向对齐。在每种情况下，一个平台发生在中间极化减少，但仍然广泛的简并。剩余的基态可以分别映射到蜂窝和正方形晶格上的二聚体模型。在倾斜的外场，我们观察到的Kasteleyn型的有序-无序转变到一个平台在饱和极化和消失的熵。这种转变的研究分析使用Kasteleyn矩阵和数值使用修改后的定向回路蒙特卡罗模拟。这两种情况下的质子都表现出代数衰减的相关性。此外，还讨论了结构静力因子的特点。
英文摘要：
The protons in water ice are subject to so called \emph{ice rules} resulting in an extensive ground state degeneracy. We study how an external electric field reduces this ground state degeneracy in hexagonal water ice I$_h$ within a minimal model. We observe polarization plateaus when the field is aligned along the $[001]$ and $[010]$ directions. In each case, one plateau occurs at intermediate polarization with reduced but still extensive degeneracy. The remaining ground states can be mapped to dimer models on the honeycomb and the square lattice, respectively. Upon tilting the external field, we observe an order-disorder transition of Kasteleyn type into a plateau at saturated polarization and vanishing entropy. This transition is investigated analytically using the Kasteleyn matrix and numerically using a modified directed-loop Monte Carlo simulation. The protons in both cases exhibit algebraically decaying correlations. Moreover, the features of the static structure factor are discussed.
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