论文标题
重新审视欧几里得动力三角剖分
Euclidean Dynamical Triangulations Revisited
论文作者
论文摘要
我们对四维量子重力的模型进行数值模拟，在该模型中，欧几里得连续指标上的路径积分是通过组合三角形的总和近似的。在固定体积时，该模型包含一个离散的爱因斯坦 - 希尔伯特项，耦合$κ$和局部度量项，耦合$β$，根据共享每个顶点的简单数量加权三角形。我们在此二维参数空间中绘制了相图，并计算出各种可观察到的可观察到的信息，以产生有关任何连续性极限性质的信息。我们的结果与一阶相变的线一致，其潜热为$κ\至\ infty $。我们在临界线路上找到了一个Hausdorff尺寸，该维度接近$ d_h = 4 $，大$κ$和一个与$ d_s = \ frac {3} {2} $在短距离时相一致的频谱维度。这些结果与早期的欧几里得动力学三角剖分模型的作品大致一致，该模型利用退化的三角剖分和/或不同的度量术语，并表明此类模型表现出一定程度的普遍性。
We conduct numerical simulations of a model of four dimensional quantum gravity in which the path integral over continuum Euclidean metrics is approximated by a sum over combinatorial triangulations. At fixed volume the model contains a discrete Einstein-Hilbert term with coupling $κ$ and local measure term with coupling $β$ that weights triangulations according to the number of simplices sharing each vertex. We map out the phase diagram in this two dimensional parameter space and compute a variety of observables that yield information on the nature of any continuum limit. Our results are consistent with a line of first order phase transitions with a latent heat that decreases as $κ\to\infty$. We find a Hausdorff dimension along the critical line that approaches $D_H=4$ for large $κ$ and a spectral dimension that is consistent with $D_s=\frac{3}{2}$ at short distances. These results are broadly in agreement with earlier works on Euclidean dynamical triangulation models which utilize degenerate triangulations and/or different measure terms and indicate that such models exhibit a degree of universality.
