Is the Two-Dimensional One-Component Plasma Exactly Solvable?

Abstract

The model under consideration is the two-dimensional (2D) one-component plasma of pointlike charged particles in a uniform neutralizing background, interacting through the logarithmic Coulomb interaction. Classical equilibrium statistical mechanics is studied by non-traditional means. The question of the potential integrability (exact solvability) of the plasma is investigated, first at arbitrary coupling constant Γvia an equivalent 2D Euclidean-field theory, and then at the specific values of Γ=2*integer via an equivalent 1D fermionic model. The answer to the question in the title is that there is strong evidence for the model being not exactly solvable at arbitrary Γbut becoming exactly solvable at Γ=2*integer. As a by-product of the developed formalism, the gauge invariance of the plasma is proven at the free-fermion point Γ=2; the related mathematical peculiarity is the exact inversion of a class of infinite-dimensional matrices.

26 pages

References in corpus (3)

• The statistical mechanics of the classical two-dimensional Coulomb gas is exactly solved
• Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime
• Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids II

Cited by in corpus (20)

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• Exact Energy Computation of the One Component Plasma on a Sphere for Even Values of the Coupling Parameter
• A Generalization of the Stillinger-Lovett Sum Rules for the Two-Dimensional Jellium
• Plasma living in a curved surface at some special temperature
• Attraction of like-charged walls with counterions only: Exact results for the 2D cylinder geometry
• Counter-Ions Near a Charged Wall: Exact Results for Disc and Planar Geometries
• Counter-ion density profile around a charged disk: from the weak to the strong association regime
• Finite-Size Effects in Non-Neutral Two-Dimensional Coulomb Fluids
• Electric double layers with modulated surface charge density: Exact 2D results
• A two-dimensional one component plasma and a test charge : polarization effects and effective potential
• Amplitude Function of Asymptotic Correlations Along Charged Wall in Coulomb Fluids
• Short-distance symmetry of pair correlations in two-dimensional jellium
• Fourth Moment of the Charge Density Induced Around A Guest Charge in Two-Dimensional Jellium
• Exact Energy Expansion of the two-dimensional Dyson Gas for Odd Values of $\Gamma /2$
• Contact value theorem for electric double layers with modulated surface charge density
• Effective interaction between guest charges immersed in 2D jellium