Debye-Hückel theory for charge symmetric Coulomb systems

It is proven that the pressure, density and correlation functions of a classical charge symmetric Coulomb system are asymptotic as the plasma parameter ε tends to zero to the approximations predicted by the Debye-Hückel theory. These approximations consist of the ideal gas term plus a term of one lower order in ε. The sine-Gordon transformation and some new correlation inequalities for the associated functional integrals are used.