Finite-size corrections to the free energy of Coulomb systems with a periodic boundary condition

Abstract

Classical Coulomb systems in d dimensions (d≥2) with a periodic boundary condition, period W, in the direction x(d)are considered. With the other directions of the confining volume of length L, it is shown that if the system is in a conducting phase, then the "strip" free energy kTfW, fW= -limL→∞L-(d-1) log Z, has the large-W expansion {Mathematical expression} where kTf∞ is the bulk free energy per unit volume, ζ(x) denotes the Riemann zeta function, and Γ(x) denotes the gamma function. With 1/W identified as kT, this result is precisely the low-temperature behavior of the free energy of a (d-1)-dimensional Debye solid. This fact is explained in terms of an equivalence between the Coulomb g..