Higher spin one-dimensional Ising lattice in arbitrary external field

Jerome Percus

Research output: Contribution to journalArticle

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, 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.

Original languageEnglish (US)
Pages (from-to)1162-1167
Number of pages6
JournalJournal of Mathematical Physics
Volume23
Issue number6
StatePublished - 1981

Fingerprint

Ising
External Field
Nearest Neighbor
Arbitrary
Spin Models
Thermodynamics
Lattice Model
Probability Density
One Dimension
Correlation Function
Random walk
Ensemble
random walk
integers
Integer
Dependent
Interaction
thermodynamics
interactions

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

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

In: Journal of Mathematical Physics, Vol. 23, No. 6, 1981, p. 1162-1167.

Research output: Contribution to journalArticle

@article{bce9941ec76d4e26973bbd5c61aae137,
title = "Higher spin one-dimensional Ising lattice in arbitrary external field",
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, 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.",
author = "Jerome Percus",
year = "1981",
language = "English (US)",
volume = "23",
pages = "1162--1167",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "6",

}

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 -