title: Equilibrium statistical mechanics of a grain boundary.
abstract: In this article we introduce, develop, and discuss the theoretical calculations required for the exact solution of a recently reported phase transition, the geodesic to zigzag transition. In this scenario the interfacial transition emerges from geometric competition between a geodesic, shortest path, configuration and a zigzag configuration which is able to reduce its energy by binding to a centrally positioned defect line. From a technical point of view the transition is unusual as it is described by a change from saddle dominated behavior to pole dominated behavior of the integral representing the partition function ratio. We also establish the precise fluctuation behavior of the interface by computing the spin magnetization at any point in the system.
authors.affiliation: Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom.
authors.forename: D B
authors.initials: DB
authors.lastname: Abraham
authors.forename: Ville
authors.initials: V
authors.lastname: Mustonen
authors.forename: A J
authors.initials: AJ
authors.lastname: Wood