Abstract
We map the classical two-dimensional one-component plasma of charged particles with coupling constant Γ an even positive integer onto a one-dimensional fermionic system. We then show that, in the thermodynamic limit of the fluid regime, translational invariance of the two-body density implies an infinite sequence of interrelations among the coefficients of its short-distance expansion. The existence of these sum rules turns out to be related to a general symmetry of the Coulomb system, providing a functional relation for the two-body density for arbitrary coupling Γ.
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Šamaj, L., Percus, J.K. A functional relation among the pair correlations of the two-dimensional one-component plasma. J Stat Phys 80, 811–824 (1995). https://doi.org/10.1007/BF02178556
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DOI: https://doi.org/10.1007/BF02178556