论文标题
在随机双子图和KPZ上的汉密尔顿路径的指数
Exponents for Hamiltonian paths on random bicubic maps and KPZ
论文作者
论文摘要
我们评估了在随机平面双子图中绘制的汉密尔顿路径各种集合的配置指数。这些指数是根据有限大小的精确枚举结果的外推估计的，并将其基于KPZ关系的理论预测进行了比较，该预测适用于其在蜂窝晶格上的常规对应物。我们表明，对这些关系的幼稚使用不会再现测量的指数，但是其应用程序中的简单修改可能会纠正观察到的差异。我们表明，需要类似的修改才能通过KPZ公式复制一些确切的指数，因为它在随机平面双子图中未加权的完全填充环的问题。
We evaluate the configuration exponents of various ensembles of Hamiltonian paths drawn on random planar bicubic maps. These exponents are estimated from the extrapolations of exact enumeration results for finite sizes and compared with their theoretical predictions based on the KPZ relations, as applied to their regular counterpart on the honeycomb lattice. We show that a naive use of these relations does not reproduce the measured exponents but that a simple modification in their application may possibly correct the observed discrepancy. We show that a similar modification is required to reproduce via the KPZ formulas some exactly known exponents for the problem of unweighted fully packed loops on random planar bicubic maps.
