Lattice Green's functions for kagome, diced and hyperkagome lattices
Statistical Mechanics
2013-11-01 v1 Mathematical Physics
math.MP
Abstract
Lattice Green's functions (LGF) and density of states (DOS) for non-interacting models on 3 related lattices are presented. The DOS and LGF at the origin for the kagome and diced lattices are rederived. Furthermore, from the form obtained for the DOS of the hyperkagome lattice, it seems highly suggestive that a closed form expression can be obtained if a particular complicated yet highly symmetrical integral can be solved. The results have been checked numerically. The continuum of energy states in the hyperkagome lattice and the appearance of a zero in the kagome lattice may be explicitly seen from the formulae obtained.
Keywords
Cite
@article{arxiv.1211.5666,
title = {Lattice Green's functions for kagome, diced and hyperkagome lattices},
author = {Vipin Kerala Varma and Hartmut Monien},
journal= {arXiv preprint arXiv:1211.5666},
year = {2013}
}