Molecular dynamics simulation of a two-dimensional system

The study of a two-dimensional system started nearly half a century ago when Peierls and Landau showed the lack of long range translational order in a two-dimensional solid. In 1968, Mermin proved that despite the absence of long range translational order, two-dimensional solids can still exhibit a different kind of long range bond orientation. During the last decade, fascinating theories were put forward to explain the role of topological defects in the melting of two-dimensional solids, starting with Kosterlizand Thouless. Recent surge of interest in melting is also due to the theoretical ideas of Hal perin, Nelson and Young. They have suggested that the transition may be fundamentally different from that observed in ordinary three-dimensional systems. Computer simulations suggest that the transition is of the usual first-order type observed in a three-dimensional system. A large body of experimental and simulation research into the two-dimensional melting followed the announcement of the KTHNY theory. In spite of all this effort, the question as to the nature of two dimensional melting remains unresolved. Recent experimental work supporting the existence of continuous melting transitions in some two-dimensional systems indicates the need for further theoretical and computational work to lead to an understanding of the experimental results. In this paper we intend to summarize and clarify the current situation with regard to research in the two-dimensional melting with an emphasis on compute simulations. The paper begins with an overview of the current status of relevant theoretical, experimental and simulation research, then a two-dimensional simulation of an ionic salt system is studied in detail. This simulation has been done by using the molecular dynamics method. The most important parameters that have been determined are: The transition temperature, the total energy of the system, the mean square displacement and the bond angle distribution. The transition temperature of the system has been specified by plotting some of these parameters as a function of temperature and time. The first order transition is observed. It is difficult to distinguish a hexa tic phase from a two-phase coexistence region