### Abstract

We consider an integer lattice in one dimension whose site variables take on the values ν = 0,1,...,D with a fixed nearest neighbor interaction but an arbitrary site-dependent external potential. By first eliminating the external potential in favor of the site probability density, an expression is found in principle for the potential as a functional of the density. This relation is worked out in detail for basic spin 1/2 model, Z_{3} lattice, random walk ensemble, and a special continuous spin model. The direct correlation function in all cases has only nearest neighbor support, and the thermodynamic potential as a functional of the density couples only nearest neighbor sites.

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

Pages (from-to) | 1162-1167 |

Number of pages | 6 |

Journal | Journal of Mathematical Physics |

Volume | 23 |

Issue number | 6 |

State | Published - 1981 |

### Fingerprint

### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*23*(6), 1162-1167.

**Higher spin one-dimensional Ising lattice in arbitrary external field.** / Percus, Jerome.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 23, no. 6, pp. 1162-1167.

}

TY - JOUR

T1 - Higher spin one-dimensional Ising lattice in arbitrary external field

AU - Percus, Jerome

PY - 1981

Y1 - 1981

N2 - We consider an integer lattice in one dimension whose site variables take on the values ν = 0,1,...,D with a fixed nearest neighbor interaction but an arbitrary site-dependent external potential. By first eliminating the external potential in favor of the site probability density, an expression is found in principle for the potential as a functional of the density. This relation is worked out in detail for basic spin 1/2 model, Z3 lattice, random walk ensemble, and a special continuous spin model. The direct correlation function in all cases has only nearest neighbor support, and the thermodynamic potential as a functional of the density couples only nearest neighbor sites.

AB - We consider an integer lattice in one dimension whose site variables take on the values ν = 0,1,...,D with a fixed nearest neighbor interaction but an arbitrary site-dependent external potential. By first eliminating the external potential in favor of the site probability density, an expression is found in principle for the potential as a functional of the density. This relation is worked out in detail for basic spin 1/2 model, Z3 lattice, random walk ensemble, and a special continuous spin model. The direct correlation function in all cases has only nearest neighbor support, and the thermodynamic potential as a functional of the density couples only nearest neighbor sites.

UR - http://www.scopus.com/inward/record.url?scp=36749117864&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749117864&partnerID=8YFLogxK

M3 - Article

VL - 23

SP - 1162

EP - 1167

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

ER -