Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma

Abstract

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 explore two applications of this formalism to study the moments of the pair correlation function of the 2dOCP on a sphere, and the distribution of radial linear statistics of the 2dOCP in the plane.

References in corpus (4)

• Fractional Quantum Hall States and Jack Polynomials
• A Generalization of the Stillinger-Lovett Sum Rules for the Two-Dimensional Jellium
• Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems
• Debye-Huckel theory for two-dimensional Coulomb systems living on a finite surface without boundaries

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• Exact Energy Computation of the One Component Plasma on a Sphere for Even Values of the Coupling Parameter
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• Finite-Size Effects in Non-Neutral Two-Dimensional Coulomb Fluids
• Electric double layers with modulated surface charge density: Exact 2D results
• Counter-ion density profile around a charged disk: from the weak to the strong association regime
• Fourth Moment of the Charge Density Induced Around A Guest Charge in Two-Dimensional Jellium
• Combinatorial Interpretation of the Scalar Products of State Vectors of Integrable Models
• Exact Energy Expansion of the two-dimensional Dyson Gas for Odd Values of $\Gamma /2$
• Effective interaction between guest charges immersed in 2D jellium