Critical resonance in the non-intersecting lattice path model

We study the phase transition in the honeycomb dimer model (equivalently, monotone non-intersecting lattice path model). At the critical point the system has a strong long-range dependence; in particular, periodic boundary conditions give rise to a resonance phenomenon, where the partition function and other properties of the system depend sensitively on the shape of the domain.The research leading to this article was conducted in part while the first author was visiting Microsoft.Mathematics Subject Classification (2000): 82B20Revised version: 7 July 2003