Surface Tension of an Ideal Dielectric-Electrolyte Boundary: Exactly Solvable Model

The model under consideration is a semi-infinite two-dimensional two-component plasma (Coulomb gas), stable against bulk collapse for the dimensionless coupling constant β < 2, in contact with a dielectric wall of dielectric constant = 0. The model is mapped onto an integrable sine-Gordon theory with a “free” Neumann boundary condition. Using recent results on a reflection relationship between the boundary Liouville and sine-Gordon theories, an explicit expression is derived for the surface tension at a rectilinear dielectric – Coulomb gas interface. This expression reproduces the Debye-Hückel β → 0 limit and the exact result at the bulk collapse border, the free-fermion point β = 2, where the surface tension keeps a finite value. The surface collapse, identified with the divergence of the surface tension, occurs at β = 3.