### Abstract

The resistance between two arbitrary grid points of several infinite lattice structures of resistors is calculated by using lattice Green's functions. The resistance for d dimensional hypercubic, rectangular, triangular, and honeycomb lattices of resistors is discussed in detail. Recurrence formulas for the resistance between arbitrary lattice points of the square lattice are given. For large separation between nodes the asymptotic form of the resistance for a square lattice and the finite limiting value of the resistance for a simple cubic lattice are calculated. The relation between the resistance of the lattice and the van Hove singularity of the tight-binding Hamiltonian is given. The Green's function method used in this paper can be applied in a straightforward manner to other types of lattice structures and can be useful didactically for introducing many concepts used in Condensed matter physics.

Original language | English |
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Pages (from-to) | 896-906 |

Number of pages | 11 |

Journal | American Journal of Physics |

Volume | 68 |

Issue number | 10 |

Publication status | Published - Oct 2000 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Application of the lattice Green's function for calculating the resistance of an infinite network of resistors.** / Cserti, J.

Research output: Contribution to journal › Article

*American Journal of Physics*, vol. 68, no. 10, pp. 896-906.

}

TY - JOUR

T1 - Application of the lattice Green's function for calculating the resistance of an infinite network of resistors

AU - Cserti, J.

PY - 2000/10

Y1 - 2000/10

N2 - The resistance between two arbitrary grid points of several infinite lattice structures of resistors is calculated by using lattice Green's functions. The resistance for d dimensional hypercubic, rectangular, triangular, and honeycomb lattices of resistors is discussed in detail. Recurrence formulas for the resistance between arbitrary lattice points of the square lattice are given. For large separation between nodes the asymptotic form of the resistance for a square lattice and the finite limiting value of the resistance for a simple cubic lattice are calculated. The relation between the resistance of the lattice and the van Hove singularity of the tight-binding Hamiltonian is given. The Green's function method used in this paper can be applied in a straightforward manner to other types of lattice structures and can be useful didactically for introducing many concepts used in Condensed matter physics.

AB - The resistance between two arbitrary grid points of several infinite lattice structures of resistors is calculated by using lattice Green's functions. The resistance for d dimensional hypercubic, rectangular, triangular, and honeycomb lattices of resistors is discussed in detail. Recurrence formulas for the resistance between arbitrary lattice points of the square lattice are given. For large separation between nodes the asymptotic form of the resistance for a square lattice and the finite limiting value of the resistance for a simple cubic lattice are calculated. The relation between the resistance of the lattice and the van Hove singularity of the tight-binding Hamiltonian is given. The Green's function method used in this paper can be applied in a straightforward manner to other types of lattice structures and can be useful didactically for introducing many concepts used in Condensed matter physics.

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UR - http://www.scopus.com/inward/citedby.url?scp=0034422699&partnerID=8YFLogxK

M3 - Article

VL - 68

SP - 896

EP - 906

JO - American Journal of Physics

JF - American Journal of Physics

SN - 0002-9505

IS - 10

ER -