论文标题
点组$ \ boldsymbol {c_ {6v}} $的通用渐近相关功能以及三角晶格$ \ boldsymbol {q} $的观察
Universal asymptotic correlation functions for point group $\boldsymbol{C_{6v}}$ and an observation for triangular lattice $\boldsymbol{Q}$-state Potts model
论文作者
论文摘要
我们研究了具有$ c_ {6v} $对称性的非临界系统的渐近相关函数的通用形式，该函数是$ c_ {4v} $ symetry in Phys。〜ev.与$ c_ {4v} $ case不同，只有一个仅包含两个免费参数的最小形式：标准化常数和模量。使用此形式作为构建块，我们可以为最小值构建下一个渐近形式。我们对过渡温度上方的三角形晶格$ q $ q $ q $ q $ q $ q $ q $ q $ q $ q的大规模蒙特卡洛模拟，并成功获得数值证据，以支持最小形式对晶格模型的广泛适用性，包括不可分析的模型。根据计算出的最小形式，我们得出了由蜂窝晶格potts模型中的平衡晶体的普遍形状，该模型由代数曲线的代数曲线描述为1。示例，$ c_ {6v} $和$ c_ {4v} $。
We investigate universal forms for asymptotic correlation functions of off-critical systems that possess $C_{6v}$ symmetry following the argument for $C_{4v}$ symmetry in Phys.~Rev.~E{\bf 102},~032141. Unlike the $C_{4v}$ case, a minimal form exists that contains only two free parameters: the normalization constant and modulus. Using this form as a building block, we can construct next asymptotic forms to the minimal one. We perform large-scale Monte Carlo simulations of the triangular lattice $Q$-state Potts model above the transition temperature and successfully obtain numerical evidence to support a wide applicability of the minimal form to lattice models, including unsolvable ones. From the calculated minimal form, we derive the universal shape of equilibrium crystals in the honeycomb lattice Potts model described by an algebraic curve of genus 1. Although the curve differs from those obtained in the $C_{4v}$ case, the latters also have genus 1. We indicate that the birational equivalence concept can play an important role in comparing asymptotic forms for different point group symmetries, for example, $C_{6v}$ and $C_{4v}$.
