The phases of two-dimensional matter,their transitions,and solid-state stability: A perspective via computer simulation of simple atomic systems

An extensive computer simulation investigation of the structure, thermodynamics and phase stability of the two-dimensional Lennard-Jones system is presented, with special emphasis on the low-pressure melting regime of the phase diagram. This investigation includes isobaric-isothermal Monte Carlo simulations of the various phases of the two-dimensional Lennard-Jones system and of the melting and vaporization processes in configuration space, the isodensity-isothermal Monte Carlo simulations of two-phase coexistence between crystal and liquid and between liquid and vapor, the determination of the phase diagram, the establishment of the thermodynamic melting temperature, and the determination of the physical significance of the Kosterlitz-Thouless-Feynman dislocation model for melting in relation to the stability of the crystalline phase. I conclude that th phase diagram of the Lennard-Jones system in two dimensions is qualitatively similar to that in three dimensions. Finally, I present a new simulation method for doing molecular dynamics at constant pressure and/or constant temperature, and employ this method to study the temporal-spatial evolution of two-dimensional melting and vaporization.