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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics