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Various strong coupling theories of the one-component plasma havesuccessfully predicted the thermodynamic and structural properties byseparating the Coulomb potential into short- and long-ranged parts in {\itshapead hoc} ways. Moreover, it has been demonstrated that the density-densitycorrelation function in a mimic system with only the short-ranged interactionsresembles that of the full Coulomb system, revealing that the van der Waalspicture applies to the strongly coupled Coulomb systems. Here we provide avariational theory forming the basis of the van der Waals picture. Our approachprovides hybrid formulations which combine both the liquid state theory andstatistical field theory; essential use is made of the coarse-grained systemwith only long-raged part of Coulomb interactions as a reference system inintroducing both lower bound variational principle and strong couplingexpansion.

A variational principle behind van der Waals picture of strongly coupled plasmas