### Abstract

We study a classical charge symmetric system with an external charge distribution q in three dimensions in the limit that the plasma parameter e{open}→ zero. We prove that if q is scaled appropriately then the correlation functions converge pointwise to those of an ideal gas in the external mean field Ψ(x) where Ψ is given by-ΔΨ+ 2z sinh(βΨ) =q This is the mean field equation of Debye and Hückel. The proof uses the sine-Gordon transformation, the Mayer expansion, and a correlation inequality.

Original language | English (US) |
---|---|

Pages (from-to) | 529-559 |

Number of pages | 31 |

Journal | Journal of Statistical Physics |

Volume | 37 |

Issue number | 5-6 |

DOIs | |

State | Published - Dec 1984 |

Externally published | Yes |

### Fingerprint

### Keywords

- Coulomb systems
- Debye-Hückel theory
- Mayer expansion
- mean field theory
- sine-Gordon transformation

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*37*(5-6), 529-559. https://doi.org/10.1007/BF01010494

**Mean field theory for Coulomb systems.** / Kennedy, Thomas G.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 37, no. 5-6, pp. 529-559. https://doi.org/10.1007/BF01010494

}

TY - JOUR

T1 - Mean field theory for Coulomb systems

AU - Kennedy, Thomas G

PY - 1984/12

Y1 - 1984/12

N2 - We study a classical charge symmetric system with an external charge distribution q in three dimensions in the limit that the plasma parameter e{open}→ zero. We prove that if q is scaled appropriately then the correlation functions converge pointwise to those of an ideal gas in the external mean field Ψ(x) where Ψ is given by-ΔΨ+ 2z sinh(βΨ) =q This is the mean field equation of Debye and Hückel. The proof uses the sine-Gordon transformation, the Mayer expansion, and a correlation inequality.

AB - We study a classical charge symmetric system with an external charge distribution q in three dimensions in the limit that the plasma parameter e{open}→ zero. We prove that if q is scaled appropriately then the correlation functions converge pointwise to those of an ideal gas in the external mean field Ψ(x) where Ψ is given by-ΔΨ+ 2z sinh(βΨ) =q This is the mean field equation of Debye and Hückel. The proof uses the sine-Gordon transformation, the Mayer expansion, and a correlation inequality.

KW - Coulomb systems

KW - Debye-Hückel theory

KW - Mayer expansion

KW - mean field theory

KW - sine-Gordon transformation

UR - http://www.scopus.com/inward/record.url?scp=0009144424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009144424&partnerID=8YFLogxK

U2 - 10.1007/BF01010494

DO - 10.1007/BF01010494

M3 - Article

AN - SCOPUS:0009144424

VL - 37

SP - 529

EP - 559

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5-6

ER -