The theoretical calculations required for the exact solution of a recently reported phase transition, the geodesic to zig-zag transition, were developed. In this scenario, the interfacial transition emerged from geometrical competition between a geodesic shortest-path configuration and a zig-zag configuration which was able to reduce its energy by binding to a centrally positioned defect line. The transition was unusual as it was described by a change from a saddle-dominated behavior to pole-dominated behavior of the integral representing the partition-function ratio. The precise fluctuation behavior of the interface was also established by computing the spin magnetization at any point in the system.

Equilibrium Statistical Mechanics of a Grain Boundary. D.B.Abraham, V.Mustonen, A.J.Wood: Physical Review E, 2005, 71[3], 036106 (9pp)