标题： 关于二维量子引力中分形维数的c相关性的数值研究 显示英文标题

标题： Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity

摘要： 我们数值研究了二维量子引力与中心电荷为 c 的物质耦合时的分形结构，其中 c 对应于$-2 \leq c \leq 1$。 我们将 Q 状态杨模型重新表述为一个可以被识别为加权渗流团簇模型的模型，并且可以在动态三角化网格上实现 Q 的连续变化，Q 与 c 相关。 通过渗流概率和易感性测量了临界耦合的 c 依赖性。 评估了量子表面的弦易感性的 c 依赖性，并且与理论预测非常吻合。 基于有限尺寸标度假设测量了分形维数的 c 依赖性，除了接近$c\approx 1$的区域外，其结果与之前提出的理论预测具有极好的一致性。 显示英文摘要

摘要： We numerically investigate the fractal structure of two-dimensional quantum gravity coupled to matter central charge c for $-2 \leq c \leq 1$. We reformulate Q-state Potts model into the model which can be identified as a weighted percolation cluster model and can make continuous change of Q, which relates c, on the dynamically triangulated lattice. The c-dependence of the critical coupling is measured from the percolation probability and susceptibility. The c-dependence of the string susceptibility of the quantum surface is evaluated and has very good agreement with the theoretical predictions. The c-dependence of the fractal dimension based on the finite size scaling hypothesis is measured and has excellent agreement with one of the theoretical predictions previously proposed except for the region near $c\approx 1$.