Abstract
A two-component Coulomb gas confined by walls made of ideal dielectric material is considered. In two dimensions at the special inverse temperature β=2, by using the Pfaffian method, the system is mapped onto a four-component Fermi field theory with specific boundary conditions. The exact solution is presented for a semi-infinite geometry of the dielectric wall (the density profiles, the correlation functions) and for the strip geometry (the surface tension, a finite-size correction of the grand potential). The universal finite-size correction of the grand potential is shown to be a consequence of the good screening properties, and its generalization is derived for the conducting Coulomb gas confined in a slab of arbitrary dimension ≥2 at any temperature.
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Jancovici, B., Šamaj, L. Coulomb Systems with Ideal Dielectric Boundaries: Free Fermion Point and Universality. Journal of Statistical Physics 104, 753–775 (2001). https://doi.org/10.1023/A:1010332822814
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DOI: https://doi.org/10.1023/A:1010332822814