A renormalization method for the evaluation of lattice sums

C. Leonard Berman, Leslie Greengard

Research output: Contribution to journalReview article

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 languageEnglish (US)
Pages (from-to)6036-6048
Number of pages13
JournalJournal of Mathematical Physics
Volume35
Issue number11
DOIs
StatePublished - Jan 1 1994

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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