2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62677We 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.28 pages, 6 figures. v4 has changes suggested by refereeProbabilityCondensed MatterCombinatorics82B20; 60C05text