https://doi.org/10.1140/epjp/s13360-021-01619-1
Regular Article
The two-site resistance of the two-dimensional ruby lattice structure
Department of Physics, Al-Hussein Bin Talal University, P.O. Box 20, 71111, Ma’an, Jordan
Received:
15
February
2021
Accepted:
27
May
2021
Published online:
4
June
2021
In this paper, the lattice Green’s function theory has been implemented to calculate the effective resistance between two arbitrary lattice sites in the two-dimensional ruby lattice structure with edges (resistors) connecting next-nearest-neighbour sites of identical resistors. Obtaining explicit resistance expressions, it is shown that the two-site resistances on ruby lattice structure with resistors connecting next-nearest-neighbour sites are expressed in terms of the resistance of a triangular lattice. For large separation between lattice points, the asymptotic forms of the resistance are calculated. As a result, our analysis has been used to solve the spanning tree problem on the ruby lattice.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
