Within the framework of string field theory the intrinsic Hausdorff dimensiond_H of the ensemble of surfaces in two-dimensional quantum gravity has recentlybeen claimed to be 2m for the class of unitary minimal models (p = m+1,q = m).This contradicts recent results from numerical simulations, which consistentlyfind d_H approximatly 4 in the cases m = 2, 3, 5 and infinity. The string fieldcalculations rely on identifying the scaling behavior of geodesic distance andarea with respect to a common length scale l. This length scale is introducedby formulating the models on a disk with fixed boundary length l. In this paperwe study the relationship between the mean area and the boundary length forpure gravity and the Ising model coupled to gravity. We discuss how thisrelationship is modified by relevant perturbations in the Ising model. Wediscuss how this leads to a modified value for the Hausdorff dimension.
展开▼
机译：在弦场理论的框架内，最近对于二维最小引力模型（p = m + 1，q = m）一类，二维量子引力的表面整体的固有Hausdorff维数_H被宣称为2m。数值模拟的结果，在m = 2、3、5和无穷大的情况下，d_H始终一致地近似为4。字符串字段计算依赖于确定测地距离和区域相对于公共长度比例尺l的缩放行为。通过在具有固定边界长度l的磁盘上公式化模型来引入此长度比例尺。在本文中，我们研究了纯重力的平均面积与边界长度之间的关系以及与重力耦合的伊辛模型。我们讨论了如何通过Ising模型中的相关扰动来修改此关系。我们将讨论这如何导致修改Hausdorff尺寸的值。
展开▼
