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 $\beta<2$, 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-H\"uckel $\beta \to 0$ limit and the exact result at the bulk collapse border, the free-fermion point $\beta =2$, where the surface tension keeps a finite value. The surface collapse, identified with the divergence of the surface tension, occurs at $\beta =3$.