Renormalized finite-cluster method for lattice models. I. Site renormalization and star cluster expansions
William J. Shugard, John D. Weeks
We give a simple derivation of a finite cluster expansion for the free energy of a general inhomogeneous lattice system which uses only connected clusters. Two possible ways of defining these clusters are discussed in detail, one most useful for obtaining high-temperature series expansions and another low-temperature expansions. A renormalized finite cluster expansion which uses only multiply connected or star clusters follows from a Legendre transformation on the free energy in which single-site potentials are replaced as independent variables by single-site probability distribution functions. Certain special cases of these results have been known before and successfully used to derive high-temperature series expansions. The relationship of the present approach to the renormalized linked-cluster perturbation expansion used by Wortis and co-workers is discussed, and comparison is also made with the work of Rushbrook and Scoins. Truncations of the renormalized cluster expansion yield closed-form approximations which, except in the critical region, offer a systematic way of improving mean-field theory.
Physical review. B, Condensed matter•Dec 1, 1980•4 citations