Short-distance expansion of correlation functions in the charge-symmetric two-dimensional two-component plasma: Exact results

Abstract

We determine exactly the short-distance leading behavior of the density correlation functions of a two-dimensional two-component charge-symmetric Coulomb gas composed of point particles, in the whole regime of stability where the coulombic coupling $\beta <2$. More generally, we compute the short-distance behavior of the effective interaction potential between two external arbitrary charges $Q_1$ and $Q_2$ immersed in the plasma, for $\beta |Q_1|<2$ and $\beta |Q_2|<2$. We also find the short-distance asymptotics of the density profiles near a single external charge $Q$ immersed in the plasma for $\beta |Q|<2$.

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• Screening of an electrically charged particle in a two-dimensional two-component plasma at $\Gamma =2$
• Renormalized charge in a two-dimensional model of colloidal suspension from hypernetted chain approach
• Two-dimensional two-component plasma with adsorbing impurities
• Like-charge attraction in one- and two-dimensional Coulomb systems