### Abstract

A number of problems in solid state physics and materials science can be resolved by the evaluation of certain lattice sums (sums over all sites of an infinite perfect lattice of some potential energy function). One classical example, the calculation of lattice sums of circular and spherical harmonics, dates back to the last century, to Lord Rayleigh's work on computing the effective conductivity of a simple composite. While Lord Rayleigh presented an efficient asymptotic method for two-dimensional problems, he resorted to direct evaluation of the lattice sums in the three-dimensional case. More recent methods, based on Ewald summation, have been developed by Nijboer and De Wette, Schmidt and Lee, and others. In this article, a fast method for evaluating lattice sums which is based on a new renormalization identity is described.

Original language | English (US) |
---|---|

Pages (from-to) | 6036-6048 |

Number of pages | 13 |

Journal | Journal of Mathematical Physics |

Volume | 35 |

Issue number | 11 |

State | Published - 1994 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*35*(11), 6036-6048.

**A renormalization method for the evaluation of lattice sums.** / Berman, C. Leonard; Greengard, Leslie.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 35, no. 11, pp. 6036-6048.

}

TY - JOUR

T1 - A renormalization method for the evaluation of lattice sums

AU - Berman, C. Leonard

AU - Greengard, Leslie

PY - 1994

Y1 - 1994

N2 - A number of problems in solid state physics and materials science can be resolved by the evaluation of certain lattice sums (sums over all sites of an infinite perfect lattice of some potential energy function). One classical example, the calculation of lattice sums of circular and spherical harmonics, dates back to the last century, to Lord Rayleigh's work on computing the effective conductivity of a simple composite. While Lord Rayleigh presented an efficient asymptotic method for two-dimensional problems, he resorted to direct evaluation of the lattice sums in the three-dimensional case. More recent methods, based on Ewald summation, have been developed by Nijboer and De Wette, Schmidt and Lee, and others. In this article, a fast method for evaluating lattice sums which is based on a new renormalization identity is described.

AB - A number of problems in solid state physics and materials science can be resolved by the evaluation of certain lattice sums (sums over all sites of an infinite perfect lattice of some potential energy function). One classical example, the calculation of lattice sums of circular and spherical harmonics, dates back to the last century, to Lord Rayleigh's work on computing the effective conductivity of a simple composite. While Lord Rayleigh presented an efficient asymptotic method for two-dimensional problems, he resorted to direct evaluation of the lattice sums in the three-dimensional case. More recent methods, based on Ewald summation, have been developed by Nijboer and De Wette, Schmidt and Lee, and others. In this article, a fast method for evaluating lattice sums which is based on a new renormalization identity is described.

UR - http://www.scopus.com/inward/record.url?scp=21844511115&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844511115&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21844511115

VL - 35

SP - 6036

EP - 6048

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 11

ER -