Exact energy computation of the one component plasma on a sphere for even values of the coupling parameter (Q321351)

The investigated system is a one component two dimensional plasma (2d OCP) which consists of \(N\) identical particles with the same charge confined on a two dimensional surface. The neutralizing background is made of opposite identical charges. The Boltzmann factor containing the reciprocal of the absolute temperature is now expressed as a Vandermonde determinant of \(\Gamma\) this is what makes possible to calculate the parameters, free energy and structural properties for \(N=2,3,\dots,9\) as a series \(\Gamma\) (of even values). This procedure shows the way for the comparison of the crystallization features (Wigner crystal). The whole problem is destined to study the force and effect of the model even with the application of the Metropolis model.