Meanders: Exact Asymptotics
统计力学
2009-09-25 v3 高能物理 - 理论
数学物理
组合数学
math.MP
摘要
We conjecture that meanders are governed by the gravitational version of a c=-4 two-dimensional conformal field theory, allowing for exact predictions for the meander configuration exponent \alpha=\sqrt{29}(\sqrt{29}+\sqrt{5})/12, and the semi-meander exponent {\bar\alpha}=1+\sqrt{11}(\sqrt{29}+\sqrt{5})/24. This result follows from an interpretation of meanders as pairs of fully packed loops on a random surface, described by two c=-2 free fields. The above values agree with recent numerical estimates. We generalize these results to a score of meandric numbers with various geometries and arbitrary loop fugacities.
引用
@article{arxiv.cond-mat/9910453,
title = {Meanders: Exact Asymptotics},
author = {P. Di Francesco and O. Golinelli and E. Guitter},
journal= {arXiv preprint arXiv:cond-mat/9910453},
year = {2009}
}
备注
new version with note added in proof