Expanded Vandermonde powers, Jack polynomials and the two-dimensional one-component plasma
Gabriel Téllez, Departamento de Física, Universidad de Los Andes, Bogotá, Colombia
The two-dimensional one-component plasma (2dOCP) is a system of N mobile particles of the same charge q on a surface with a neutralising background. The Boltzmann factor of the 2dOCP at temperature T can be expressed as a Vandermonde determinant to the power Gamma = q^2/(k_B T). Recent advances in the theory of symmetric and anti-symmetric Jack polymonials provide an efficient way to expand this power of the Vandermonde in their monomial basis, allowing the computation of several thermodynamic and structural properties of the 2dOCP for N values up to 14 and Gamma equal to 4, 6 and 8. In this work, we present some applications of this formalism.