Boundary transitions of the O(n) model on a dynamical lattice

详细信息    查看全文

• 作者：Jean-Emile Bourgine ; Kazuo Hosomichi ; Ivan Kostov
• 关键词：Boundary ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TVC-4YB78WT-2&_mathId=mml13&_user=10&_cdi=5531&_pii=S0550321310000751&_rdoc=3&_issn=05503213&_acct=C000050221&_version=1&_userid=1
• 刊名：Nuclear Physics B
• 出版年：2010
• 出版时间：21 June 2010
• 年：2010
• 卷：832
• 期：3
• 页码：462-499
• 全文大小：429 K

文摘

We study the anisotropic boundary conditions for the dilute O(n) loop model with the methods of 2D quantum gravity. We solve the problem exactly on a dynamical lattice using the correspondence with a large N matrix model. We formulate the disk two-point functions with ordinary and anisotropic boundary conditions as loop correlators in the matrix model. We derive the loop equations for these correlators and find their explicit solution in the scaling limit. Our solution reproduces the boundary phase diagram and the boundary critical exponents obtained recently by Dubail, Jacobsen and Saleur, except for the cusp at the isotropic special transition point. Moreover, our solution describes the bulk and the boundary deformations away from the anisotropic special transitions. In particular it shows how the anisotropic special boundary conditions are deformed by the bulk thermal flow towards the dense phase.