Higher-Order Airy Scaling in Deformed Dyck Paths

详细信息    查看全文

• 作者：Nils Haug ; Adri Olde Daalhuis ; Thomas Prellberg
• 关键词：Vesicles ; Saddle point method ; Basic hypergeometric series ; Exactly solvable models ; Multicritical point ; Phase transition
• 刊名：Journal of Statistical Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：166
• 期：5
• 页码：1193-1208
• 全文大小：786KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics;
• 出版者：Springer US
• ISSN：1572-9613
• 卷排序：166

文摘

We introduce a deformed version of Dyck paths (DDP), where additional to the steps allowed for Dyck paths, ‘jumps’ orthogonal to the preferred direction of the path are permitted. We consider the generating function of DDP, weighted with respect to their half-length, area and number of jumps. This represents the first example of an exactly solvable two-dimensional lattice vesicle model showing a higher-order multicritical point. Applying the generalized method of steepest descents, we see that the associated two-variable scaling function is given by the logarithmic derivative of a generalized (higher-order) Airy integral.