Lower bound for the segregation energy in the Falicov-Kimball model
Strongly Correlated Electrons
2009-11-07 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
In this work, a lower bound for the ground state energy of the Falicov-Kimball model for intermediate densities is derived. The explicit derivation is important in the proof of the conjecture of segregation of the two kinds of fermions in the Falicov-Kimball model, for sufficiently large interactions. This bound is given by a bulk term, plus a term proportional to the boundary of the region devoid of classical particles. A detailed proof is presented for density n=1/2, where the coefficient 10^(-13) is obtained for the boundary term, in two dimensions. With suitable modifications the method can also be used to obtain a coefficient for all densities.
Cite
@article{arxiv.cond-mat/0211183,
title = {Lower bound for the segregation energy in the Falicov-Kimball model},
author = {Pedro S. Goldbaum},
journal= {arXiv preprint arXiv:cond-mat/0211183},
year = {2009}
}
Comments
8 pages, 2 figures