Geometrical defects in two-dimensional melting of many-particle Yukawa systems.

We present a theoretical polygon construction analysis of two-dimensional melting and freezing transitions in many-particle Yukawa systems. Two-dimensional melting transitions can be characterized as proliferation of geometrical defects--nontriangular polygons, obtained by removing unusually long bonds in the triangulation of particle positions. A liquid state is characterized by the temperature-independent number of quadrilaterals and linearly increasing number of pentagons. We analyze specific types of vertices, classified by the type and distribution of polygons surrounding them, and determine temperature dependencies of their concentrations. Solid-liquid phase transitions are followed by the peaks in the abundances of certain types of vertices.