1995/03/18 by B. Jancovici, G. Téllez, G. Tellez · 34 citations
Materials Science · Mathematics · Physics and Astronomy · #Conductor #Coulomb #Electric potential energy #Gaussian #Ideal (ethics) #Massless particle #Nonlinear Partial Differential Equations #Simple (philosophy) #Theoretical and Computational Physics #Thermal properties of materials #cond-mat
paper · pdf · doi:10.1007/bf02179788
published in Journal of Statistical Physics 82(3-4), 609-632 (Springer Science+Business Media) · 26 pages,TEX
arxiv created 1995/03/18 · openalex publication_date 1996/02/01 · openalex created_date 2016/06/24 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05
The grand potential of a classical Coulomb system has universal finite-size corrections similar to the ones which occur in the free energy of a simple critical system : the massless Gaussian field. Here, the Coulomb system is assumed to be confined by walls made of an ideal conductor material; this choice corresponds to simple (Dirichlet) boundary conditions for the Gaussian field. For a d-dimensional (d>or=2) Coulomb system confined in a slab of thickness W, the grand potential (in units of kT) per unit area has the universal term Gamma(d/2) zeta(d)/2d pid/2Wd-1. For a two-dimensional Coulomb system confined in a disk of radius R, the grand potential (in units of kT) has the universal term (1/6) ln R. These results, of general validity, are checked on two-dimensional solvable models.