Publication : t99/126
Meanders: exact asymptotics
Di Francesco P. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)Golinelli O. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Guitter E. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Abstract:Année de publication : 2000
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.
Revue : Nucl. Phys. B 570 699-712 (2000)
DOI : 10.1016/S0550-3213(99)00753-1
Preprint : arXiv:cond-mat/9910453
Langue : Anglais
Fichier(s) à télécharger :
nucl_phys_b-570-699.pdf
