This Letter reports investigations by molecular dynamics of the melting transition of a two-dimensional one-component plasma consisting of 511 particles with logarithmic interactions confined to a disk. Evidence is presented for a weak first-order transition occurring at T^ = ^V^r^ with r^ ^ 142 and with a melting entropy =^0.17 K. This small entropy is attributed to important premelting phenomena which are cooperative, cyclic permutations of six and more particles as revealed by labeling experiments.PACS numbers: 64.70.Dv, 52.25.Kn, 61.20.JaThe first investigation by molecular dynamics of the melting transition of the two-dimensional one-component plasma (2D-OCP) was carried out by de Leeuw and Perram/ Using periodic boundary conditions, they reported strong evidence of a first-order transition occurring at T^ c-135. A value of r^ c-140 has been obtained by Caillol et al,'^ They compared the free energy of the harmonic crystal with the free energy resulting from integrating internal energies from a Monte Carlo simulation of particles confined to the surface of a sphere with respect to T starting from the r=2 result. Using for the fluid phase a careful extrapolation of the free energy calculated for a small number of particles confined to a disk, Johannesen and Merlini^ gave an estimate of r^ c-137. In this Letter, we report extensive molecular dynamics investigations of the coexistence and premelting regions for the 2D-OCP. Following individual particle histories shows the importance of cooperative motions, strikingly reminiscent of phenomena occurring in hard-disk systems as recently reviewed by Alder, Ceperly, and Pollock/ The OCP model consists of an assembly of charged point particles immersed in a neutralizing background. In two dimensions, the Coulomb potential between two particles of charge e and separated by a distance r= |r| is -g^ln(r/l.), where L is a scaling length. For a neutral system of AT particles confined in a disk of radius R, the potential energy is^
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