Equation of states for classical Coulomb systems: Use of the Hubbard-Schofield approach

Abstract

An effective method based on Hubbard-Schofield approach [Phys. Lett. A 40, 245 (1972)] is developed to calculate the free energy of classical Coulomb systems. This method significantly simplifies the derivation of the cluster expansion. A diagrammatic representation of the cluster integrals is proposed. Simple rules providing the leading order in density n of each diagrammatic contribution are found. We calculate the n 3 contribution and recover the results at the order n 5/2 obtained by the traditional method of resummation of diverging Mayer bonds.

An accurate equation of state for the one-component plasma in the low coupling regime

“…We suggest to reexamine the details of the calculations of reference [4]. The functional Dependance in Γ of equation (2.1) is probably correct but misprints in one of the p i for either i = 5, 6 or i = 7 are likely.…”

“…In any case, the long-range nature of the interaction potential between two ionic charges causes Mayer graphs to diverge [1]. A field theoretical diagrammatic representation of cluster integrals has been proposed recently in [4] to avoid complicated chain resummations in an attempt to treat the Γ expansion of the classical Coulomb system in a more controlled and systematic way. In this interesting paper the final expansion obtained by the author improves earlier and seminal analytical results of Cohen et al [2,3] obtained by traditional diagrammatic expansions and resummations.…”

“…In the very low coupling regime, the virial expansion supplemented by well documented resummation methods, as the well-known Debye-Hückel (DH) theory [2] and its extensions (see e.g. Cohen [3] and, more recently, Ortner [4] expansions for instance)…”

The classical equation of state of fully ionized plasmas

“…Among the presently known formulas, to our knowledge the equation (45) represents the first equation of the excess free energy of electronion-plasmas until the third virial coefficient in the classical form for effective potential; Our results include terms of the higher order of the plasma parameter. ortner 20 obtained the excess free energy until the third virial coefficient for coulomb potential only. The excess free energy of ortner 20 is in agreement with the corresponding terms in our results for the coulomb potential.…”

“…ortner 20 obtained the excess free energy until the third virial coefficient for coulomb potential only. The excess free energy of ortner 20 is in agreement with the corresponding terms in our results for the coulomb potential. The results are used to derive the equation of state; among the presently known formulas, to our knowledge the classical equation of state (76) and (89) represent the first formulas of the classical equation of state of electron-ion-plasmas until the third virial coefficient for effective potential.…”