具有指向矢的球面模型
Spherical surface models with directors
摘要：
对一个三角球面模型进行了数值研究，结果表明该模型经历了光滑相和塌缩相之间的相变。该模型是通过使用的导演场，这是假设有一个与表面的法线相互作用定义。导向器和曲面之间的交互作用保持曲面形状。指向矢场在二维微分几何中没有定义，这与传统的表面模型形成鲜明对比，在传统的表面模型中，表面形状仅由曲率能保持。我们还表明，相互作用使Nambu-Goto模型定义良好，其中的键势是由三角形的面积; Nambu-Goto模型是众所周知的，即使是在传统的二维弯曲能包括在哈密顿量的一个不明确的。
英文摘要：
A triangulated spherical surface model is numerically studied, and it is shown that the model undergoes phase transitions between the smooth phase and the collapsed phase. The model is defined by using a director field, which is assumed to have an interaction with a normal of the surface. The interaction between the directors and the surface maintains the surface shape. The director field is not defined within the two-dimensional differential geometry, and this is in sharp contrast to the conventional surface models, where the surface shape is maintained only by the curvature energies. We also show that the interaction makes the Nambu-Goto model well-defined, where the bond potential is given by the area of triangles; the Nambu-Goto model is well-known as an ill-defined one even when the conventional two-dimensional bending energy is included in the Hamiltonian.
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