Matière et Systèmes Complexes (MSC), UMR 7057 CNRS & Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France.
Phys Rev Lett. 2019 Nov 1;123(18):188001. doi: 10.1103/PhysRevLett.123.188001.
Many systems, including biological tissues and foams, are made of highly packed units having high deformability but low compressibility. At two dimensions, these systems offer natural tesselations of a plane with fixed density, in which transitions from ordered to disordered patterns are often observed, in both directions. Using a modified cellular Potts model algorithm that allows rapid thermalization of extensive systems, we numerically explore the order-disorder transition of monodisperse, two-dimensional cellular systems driven by thermal agitation. We show that the transition follows most of the predictions of Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory developed for melting of 2D solids, extending the validity of this theory to systems with many-body interactions. In particular, we show the existence of an intermediate hexatic phase, which preserves the orientational order of the regular hexagonal tiling but loses its positional order. In addition to shedding light on the structural changes observed in experimental systems, our study shows that soft cellular systems offer macroscopic systems in which the KTHNY melting scenario can be explored, in the continuation of Bragg's experiments on bubble rafts.
许多系统，包括生物组织和泡沫，都是由高度堆积的单元组成的，这些单元具有高变形性但低可压缩性。在二维空间中，这些系统提供了一种固定密度的平面自然镶嵌，在这种镶嵌中，从有序到无序的图案经常在两个方向上发生转变。我们使用一种改进的元胞 Potts 模型算法，该算法允许对广泛的系统进行快速热化，从而数值研究了由热扰动驱动的单分散二维元胞系统的有序-无序转变。我们表明，该转变遵循了为二维固体熔化开发的 Kosterlitz-Thouless-Halperin-Nelson-Young（KTHNY）理论的大部分预测，将该理论的有效性扩展到具有多体相互作用的系统。特别是，我们展示了存在中间的六方相，它保留了规则六边形镶嵌的取向序，但失去了位置序。除了阐明实验系统中观察到的结构变化外，我们的研究表明，软细胞系统提供了宏观系统，在这些系统中可以探索 KTHNY 熔化情景，这延续了布拉格关于气泡筏的实验。
