Open AccessENUMERATION OF DIMER CONFIGURATIONS ON A FRACTAL LATTICE
Author(s) -
Dušanka Marčetić,
Sunčica Elezović Hadžić,
Ivan Živić
Publication year - 2018
Publication title -
contemporary materials
Language(s) - English
Resource type - Journals
eISSN - 1986-8677
pISSN - 1986-8669
DOI - 10.7251/comen1802115m
Subject(s) - dimer , fractal , enumeration , lattice (music) , statistical physics , adsorption , diatomic molecule , entropy (arrow of time) , mathematics , physics , thermodynamics , molecule , chemistry , combinatorics , mathematical analysis , quantum mechanics , nuclear magnetic resonance , acoustics
In this paper, we present a solution to the close-packed dimer problem on a fractal lattice. The dimer model is canonical model in statistical physics related with many physical phenomena. Originally, it was introduced as a model for adsorption of diatomic molecules on surfaces. Here we assume that the two dimensional substrate on which the adsorption occurs is nonhomogeneous and we represent it by the modified rectangular (MR) fractal lattice. Self-similarity of the fractal lattice enables exact recursive enumeration of all close-packed dimer configurations at every stage of fractal construction. Asymptotic form for the overall number of dimer coverings is determined and entropy per dimer in the thermodynamic limit is obtained.