  We report an extensive Monte-Carlo study of the melting of the classical two
dimensional Wigner crystal for a system of point particles interacting via the
$1/r$-Coulomb potential. A hexatic phase is found in systems large enough. With
the multiple histograms method and the finite size scaling theory, we show that
the fluid/hexatic phase transition is weakly first order. No set of critical
exponents, consistent with a Kosterlitz-Thouless transition and the finite size
scaling analysis for this transition, have been found.
