Charge fluctuations in the two-dimensional one-component plasma

We study, via computer simulations, the fluctuations in the net electric ch arge in a two-dimensional, one component plasma (OCP) with uniform backgrou nd charge density -cp in a region Lambda inside a much larger overall neutr al system. Setting e = 1, this is the same as the fluctuations in N-Lambda, the number of mobile particles of charge e. As expected, the distribution of N-Lambda has, for large Lambda, a Gaussian form with a variance which gr ows only as (k) over cap /delta Lambda/, where /delta Lambda/ is the length or the perimeter of Lambda. The properties of this system depend only on t he coupling parameter Gamma = kT, which is the same as the reciprocal tempe rature in our units. Our simulations show that when the coupling parameter Gamma increases, (k) over cap(Gamma) decreases to an asymptotic value (k) o ver cap(infinity) similar to (k) over cap(2)/2 which is equal (or very clos e) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large Gamma, the characteristic length xi(L) = 2 (k) over cap/p associated with charge fluctuations behaves very differe ntly From that of the Debye length, xi(D) similar to 1/root Gamma, which it approaches as Gamma --> 0. The pair correlation function of the OCP is als o studied.