球形膜网络模型的相变
Phase transition of meshwork models for spherical membranes
摘要：
本文用正则蒙特卡罗模拟技术研究了两种网络模型。第一种模型具有弹性连接，由顶点、键和三角形组成，而第二种模型具有刚性连接，为六边形（或五边形）刚性板。在第一个模型中，仅在弹性连接处假设二维弹性，而在第二个模型中没有假设二维弯曲弹性。两种网格均为球面拓扑。我们发现，这两个模型都经历了一个一阶坍塌之间的光滑的球形阶段和崩溃阶段的过渡。在两个模型中，平滑相的Hausdorff维数都是H \simeq 2，正如预期的那样。还发现在第二个模型的坍缩阶段H \simeq 2，在第一个模型的坍缩阶段H相对大于2，但仍保持在物理边界，即，H<3。此外，第一种模型在与坍缩过渡相同的过渡点上经历了不连续的表面起伏过渡，而第二种模型经历了表面起伏的连续过渡。这表明网络模型的相结构弱依赖于结点处的弹性。
英文摘要：
We have studied two types of meshwork models by using the canonical Monte Carlo simulation technique. The first meshwork model has elastic junctions, which are composed of vertices, bonds, and triangles, while the second model has rigid junctions, which are hexagonal (or pentagonal) rigid plates. Two-dimensional elasticity is assumed only at the elastic junctions in the first model, and no two-dimensional bending elasticity is assumed in the second model. Both of the meshworks are of spherical topology. We find that both models undergo a first-order collapsing transition between the smooth spherical phase and the collapsed phase. The Hausdorff dimension of the smooth phase is H\simeq 2 in both models as expected. It is also found that H\simeq 2 in the collapsed phase of the second model, and that H is relatively larger than 2 in the collapsed phase of the first model, but it remains in the physical bound, i.e., H<3. Moreover, the first model undergoes a discontinuous surface fluctuation transition at the same transition point as that of the collapsing transition, while the second model undergoes a continuous transition of surface fluctuation. This indicates that the phase structure of the meshwork model is weakly dependent on the elasticity at the junctions.
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