FINITE-SIZE CORRECTIONS TO THE FREE-ENERGY OF COULOMB-SYSTEMS WITH A PERIODIC BOUNDARY-CONDITION

Classical Coulomb systems in d dimensions (d greater-than-or-equal-to 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 = -lim(L --> infinity)L-(d-1) log Z, has the large-W expansion [GRAPHICS] where kTf-infinity is the bulk free energy per unit volume, zeta(x) denotes the Riemann zeta function, and GAMMA(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 gas and quantum fields. Also, the expansion is verified for some exactly solved models of Coulomb systems in two dimensions.