We consider close-packed tiling models of geometric objects—a mixture of hardcore dimers and plaquettes—as a generalization of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be covered by either a dimer on a $z$ link or a plaquette in the $x\text{−}y$ plane. The space of such fully packed tilings has an extensive degeneracy. This maps onto a fracton-type “higher-rank electrostatics,” which can exhibit a plaquette-dimer liquid and an ordered phase. We analyze this theory in detail, using height representations and T-duality to demonstrate that the concomitant phase transition occurs due to the proliferation of dipoles formed by defect pairs. The resultant critical theory can be considered as a fracton version of the Kosterlitz-Thouless transition. A significant new element is its UV-IR mixing, where the low-energy behavior of the liquid phase and the transition out of it is dominated by local (short-wavelength) fluctuations, rendering the critical phenomenon beyond the renormalization group paradigm.

中文翻译：

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重整化后的分形斑块二聚体液体

我们将几何对象的密集平铺模型（硬核二聚体和斑块的混合物）视为熟悉的二聚体模型的推广。具体来说，在各向异性立方晶格上，我们要求每个位点都被$z$链接或在$X\text{-}\mathrm{是的}$飞机。这种完全包装的瓷砖的空间具有广泛的退化性。这映射到分形类型的“高级静电学”，它可以表现出斑块二聚体液体和有序相。我们详细分析了这一理论，使用高度表示和 T 对偶来证明伴随的相变是由于缺陷对形成的偶极子的扩散而发生的。由此产生的批判理论可以被认为是 Kosterlitz-Thouless 转变的分形版本。一个重要的新元素是它的UV-IR 混合，其中液相的低能行为及其转变受局部（短波长）波动的支配，使临界现象超出了重整化群范式。