Geometric frustration and the ice rule are two concepts that are intimately connected and widespread across condensed matter. The first refers to the inability of a system to satisfy competing interactions in the presence of spatial constraints. The second, in its more general sense, represents a prescription for the minimization of the topological charges in a constrained system. Both can lead to manifolds of high susceptibility and non-trivial, constrained disorder where exotic behaviors can appear and even be designed deliberately. In this Colloquium, we describe the emergence of geometric frustration and the ice rule in soft condensed matter. This Review excludes the extensive developments of mathematical physics within the field of geometric frustration, but rather focuses on systems of confined micro- or mesoscopic particles that emerge as a novel paradigm exhibiting spin degrees of freedom. In such systems, geometric frustration can be engineered artificially by controlling the spatial topology and geometry of the lattice, the position of the individual particle units, or their relative filling fraction. These capabilities enable the creation of novel and exotic phases of matter, and also potentially lead towards technological applications related to memory and logic devices that are based on the motion of topological defects. We review the rapid progress in theory and experiments and discuss the intimate physical connections with other frustrated systems at different length scales.

中文翻译：

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座谈会：冰规则和粒子冰及其以外的涌现挫败

几何挫折和冰规则是两个概念，它们紧密地联系在一起并在冷凝物中广泛分布。第一个是指系统在存在空间约束的情况下无法满足竞争性交互作用。从更一般的意义上讲，第二个代表了在受约束的系统中最小化拓扑电荷的处方。两者都可能导致高度的敏感性和非平凡的，受约束的疾病，在这些疾病中可能会出现甚至是故意设计的外来行为。在本次座谈会中，我们描述了在软性凝聚态中出现几何挫折和冰规则的现象。本评论不包括几何挫折领域内数学物理学的广泛发展，而是专注于受限的微观或介观粒子系统，这些系统以新颖的范式出现，表现出自旋自由度。在这样的系统中，可以通过控制晶格的空间拓扑和几何形状，各个粒子单元的位置或它们的相对填充率，来人为地设计几何挫折。这些功能可以创建新颖的奇异阶段的物质，并且还潜在地导致与基于拓扑缺陷运动的内存和逻辑设备相关的技术应用。我们回顾了理论和实验的快速进展，并讨论了与其他受挫系统在不同长度尺度下的紧密物理联系。可以通过控制晶格的空间拓扑和几何形状，各个粒子单元的位置或它们的相对填充率来人工设计几何挫折。这些功能可以创建新颖的奇异阶段的物质，并且还潜在地导致与基于拓扑缺陷运动的内存和逻辑设备相关的技术应用。我们回顾了理论和实验的快速进展，并讨论了与其他受挫系统在不同长度尺度下的紧密物理联系。可以通过控制晶格的空间拓扑和几何形状，各个粒子单元的位置或它们的相对填充率来人工设计几何挫折。这些功能可以创建新颖的奇异阶段的物质，并且还潜在地导致与基于拓扑缺陷运动的内存和逻辑设备相关的技术应用。我们回顾了理论和实验的快速进展，并讨论了与其他受挫系统在不同长度尺度下的紧密物理联系。并且还可能导致基于拓扑缺陷运动的与内存和逻辑设备相关的技术应用。我们回顾了理论和实验的快速进展，并讨论了与其他受挫系统在不同长度尺度下的紧密物理联系。并且还可能导致基于拓扑缺陷运动的与内存和逻辑设备相关的技术应用。我们回顾了理论和实验的快速进展，并讨论了与其他受挫系统在不同长度尺度下的紧密物理联系。