Melting in Two Dimensions

William Swope
IBM Corporation
Almaden Research Center
San Jose, California

The nature of the solid to liquid phase transition for idealized systems of interacting point particles in two dimensions is of interest because of its possible relationship to several experimental systems and because of an intriguing possibility suggested by Halperin and Nelson and by Young in 1979 (based on work of Kosterlitz and Thouless reported in 1973) that two-dimensional melting from a solid to a liquid could occur, not by a first order transition, but by a sequence of two second order transitions and could involve an intermediate hexatic phase. Computer simulations provide a theoretical technique for investigating this problem, but such studies have proven to be difficult and the results not necessarily conclusive.

This speaker reviewed some of the controversy and reported on some computer simulations that have been performed on idealized systems of particles to shed new light on the issue. In particular, it was discovered that a proper treatment of the transition needs to include the effect of vacancy concentrations on the stability of the solid near the transition.