无开边三角晶格的皱曲过渡：一个改进的折叠规则的影响
Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule
摘要：
本文用转移矩阵方法研究了三维离散空间中三角形格点的折叠问题。该模型是由Bowick及其同事作为聚合膜在热平衡中的离散化版本引入的。折叠规则（约束）与开边界条件不相容，模拟是在开边界条件下进行的。在本文中，我们提出了一个修改后的约束，这是兼容的边界条件，技术上，平移不变性的恢复导致大量减少的传输矩阵的大小。处理团簇尺寸L \le 7，我们分析了弯曲刚度K在很宽范围内的皱曲转变的奇异性。我们在K=0.206（2），-0.32（1）和-0.76（10）处观察到一系列皱曲转变。在每个转变点，我们分别将潜热估计为Q=0.356（30）、0.08（3）和0.05（5）。
英文摘要：
Folding of the triangular lattice in a discrete three-dimensional space is investigated by means of the transfer-matrix method. This model was introduced by Bowick and co-workers as a discretized version of the polymerized membrane in thermal equilibrium. The folding rule (constraint) is incompatible with the periodic-boundary condition, and the simulation has been made under the open-boundary condition. In this paper, we propose a modified constraint, which is compatible with the periodic-boundary condition; technically, the restoration of translational invariance leads to a substantial reduction of the transfer-matrix size. Treating the cluster sizes L \le 7, we analyze the singularities of the crumpling transitions for a wide range of the bending rigidity K. We observe a series of the crumpling transitions at K=0.206(2), -0.32(1), and -0.76(10). At each transition point, we estimate the latent heat as Q=0.356(30), 0.08(3), and 0.05(5), respectively.
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