First-order phase transition of fixed connectivity surfaces

We report numerical evidence of the discontinuous transition of a tethered membrane model which is defined within a framework of the membrane elasticity of Helfrich. Two kinds of phantom tethered membrane models are studied via the canonical Monte Carlo simulation on triangulated fixed connectivity surfaces of spherical topology. One surface model is defined by the Gaussian term and the bending energy term, and the other, which is tensionless, is defined by the bending energy term and a hard wall potential. The bending energy is defined by using the normal vector at each vertex. Both models undergo the first-order phase transition characterized by a gap of the bending energy. The phase structure of the models depends on the choice of discrete bending energy.

我们报告了在赫尔弗里希（Helfrich）膜弹性框架内定义的系链膜模型不连续转变的数值证据。通过在具有球形拓扑的三角化固定连通表面上进行正则蒙特卡罗模拟，研究了两种幻影系链膜模型。一种表面模型由高斯项和弯曲能项定义，另一种无张力的模型由弯曲能项和硬壁势定义。弯曲能是通过每个顶点处的法向量来定义的。这两种模型都经历了以弯曲能间隙为特征的一级相变。模型的相结构取决于离散弯曲能的选择。