Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime

Details Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime

2003-09-19

arxiv.org/abs/cond-mat/0309476v2

J. Phys. A: Math. Gen. 37, 2121 (2004)

Physics

Condensed Matter

Statistical Mechanics

v1: 14 pages, v2: 20 pages, added a new appendix (appendix B)

Scientific paper

10.1088/0305-4470/37/6/012

It has been argued that for a finite two-dimensional classical Coulomb system of characteristic size $R$, in its conducting phase, as $R\to \infty $ the total free energy (times the inverse temperature $\beta$) admits an expansion of the form: $\beta F=AR^{2}+BR+{1/6}\chi \ln R,$ where $\chi $ is the Euler characteristic of the manifold where the system lives. 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 to obtain these finite-size corrections at the Debye--H\"uckel 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 examples we find explicitly the grand potential expansion for a Coulomb system confined in a disk and in an annulus with ideal conductor walls.

Affiliated with

Also associated with

No associations

Rating

Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite-Size Corrections for Coulomb Systems in the Debye-Huckel Regime will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-276123