二维晶格上自组装刚性杆的临界行为：Bethe-Peierls近似和蒙特卡罗模拟
Critical behavior of self-assembled rigid rods on two-dimensional lattices: Bethe-Peierls approximation and Monte Carlo simulations
摘要：
本文研究了可逆地转变成相对于基底取向受限的线性链的吸附单体的临界行为。在这里考虑的模型，这是被称为自组装刚性杆（SAARs）模型，表面是由一个二维晶格和连续的取向转变发生作为温度和覆盖的函数。通过蒙特卡罗模拟和有限尺寸标度分析，得到了正方形、三角形和蜂窝状晶格的相图。数值计算结果与Bethe-Peierls关于正方形和三角形晶格取向转变的分析预测进行了比较。相图的分析，以及临界平均棒长的行为，表明该模型的临界性能不依赖于在低温（覆盖）的晶格结构，揭示了在这个政权的一维行为。最后，普遍性类的SAARs模型，这一直是有争议的，已被重新审视。
英文摘要：
The critical behavior of adsorbed monomers that reversibly polymerize into linear chains with restricted orientations relative to the substrate has been studied. In the model considered here, which is known as self-assembled rigid rods (SAARs) model, the surface is represented by a twodimensional lattice and a continuous orientational transition occurs as a function of temperature and coverage. The phase diagrams were obtained for the square, triangular and honeycomb lattices by means of Monte Carlo simulations and finite-size scaling analysis. The numerical results were compared with Bethe-Peierls analytical predictions about the orientational transition for the square and triangular lattices. The analysis of the phase diagrams, along with the behavior of the critical average rod lengths, showed that the critical properties of the model do not depend on the structure of the lattice at low temperatures (coverage), revealing a one-dimensional behavior in this regime. Finally, the universality class of the SAARs model, which has been subject of controversy, has been revisited.
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