Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids

Details Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids

2000-04-03

arxiv.org/abs/cond-mat/0004017v1

J. Stat. Phys. 100 (2000) 949-967

Physics

Condensed Matter

Statistical Mechanics

22 pages

Scientific paper

In a Coulomb fluid confined to a domain $V$, the dielectric susceptibility tensor $\chi_V$ depends on the shape of $V$, even in the thermodynamic $V\to\infty$ limit. This paper deals with the classical two-dimensional one-component plasma formulated in an elliptic $V$-domain, equilibrium statistical mechanics is used. For the dimensionless coupling constant $\Gamma =$ even positive integer, the mapping of the plasma onto a discrete one-dimensional anticommuting-field theory provides a new sum rule. This sum rule confirms the limiting value of $\chi_V$ predicted by macroscopic electrostatics and gives the finite-size correction term to $\chi_V$.

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