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# Accurate first-principle equation of state for the One-Component Plasma

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### Abstract

Accurate "first-principle" expressions for the excess free energy $$F_{ex}$$ and internal energy $$U_{ex}$$ of the classical one-component plasma (OCP) are obtained. We use the Hubbard-Schofield transformation that maps the OCP Hamiltonian onto the Ising-like Hamiltonian, with coefficients expressed in terms of equilibrium correlation functions of a reference system. We use the ideal gas as a reference system for which all the correlation functions are known. Explicit calculations are performed with the high-order terms in the Ising-like Hamiltonian omitted. For small values of the plasma parameter $$\Gamma$$ the Debye-Huckel result for $$F_{ex}$$ and $$U_{ex}$$ is recovered. For large $$\Gamma$$ these depend linearly on $$\Gamma$$ in accordance with the Monte Carlo findings for the OCP. The MC data for the internal energy are reproduced fairly well by the obtained analytical expression.

### Most cited references4

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### Equation of state of the one-component plasma derived from precision Monte Carlo calculations

(1990)
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### Thermal energy of the crystalline one-component plasma from dynamical simulations

(1993)
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### Analytic fit to the one-component-plasma structure factor

(1991)
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### Author and article information

###### Journal
27 May 1998
cond-mat/9805358
10.1002/ctpp.2150380403
100598
15 pages, 2 figures, to appear in Contrib. Plasma Phys., v.38 N4, (1998)
cond-mat.stat-mech

Condensed matter