Relaxation and fluctuation effects near the melting transition in a two-dimensional solid

A molecular-dynamics simulation was used to examine the approach to equilibrium of a two-dimensional solid near the melting transition. The system examined consisted of 256 particles interacting through an $r^{-5\mathrm{}}$ repulsive potential. It was found that near the transition the behavior is characterized by both increasing relaxation times and increasing thermodynamic fluctuations. No true metastable states were observed. This behavior appears to be the critical slowing down that accompanies continuous transitions, supporting the view that melting in two dimensions, at least under some circumstances, is continuous. Estimates of the effects of those fluctuations which are suppressed because of the finite size of the system further supports this view. The transition temperature was found to be consistent with the Kosterlitz-Thouless dislocation hypothesis for melting but the system was too small to make any reliable statements about the existence of the hexatic phase proposed by Nelson and Halperin.