2003/09/30 by Aldemar Torres, Gabriel Téllez, Gabriel Tellez
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Electrostatics and Colloid Interactions #Quantum and Classical Electrodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/37/6/012
published as J. Phys. A: Math. Gen. 37, 2121 (2004) · v1: 14 pages, v2: 20 pages, added a new appendix (appendix B)
arxiv created 2003/11/21 · openalex publication_date 2004/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
It has been argued that for a finite two-dimensional classical Coulomb system of characteristic size R , in its conducting phase, as R → ∞ the total free energy (times the inverse temperature β) admits an expansion of the form: , where χ is the Euler characteristic of the manifold where the system exists. The first two terms represent the bulk free energy and the surface free energy, respectively. The coefficients A and B are non-universal but the coefficient of ln R is universal: it does not depend on the detail of the microscopic constitution of the system (particle densities, temperature, etc). By doing the usual Legendre transform this universal finite-size correction is also present in the grand potential. The explicit form of the expansion has been checked for some exactly solvable models for a special value of the coulombic coupling. In this paper we present a method for obtaining these finite-size corrections in the Debye–Hückel regime. It is based on the sine-Gordon field theory to find an expression for the grand canonical partition function in terms of the spectrum of the Laplace operator. As an example we find explicitly the grand potential expansion for a Coulomb system confined in a disc and in an annulus with ideal conductor walls.