Epstein zeta method for many-body lattice sums
Published in arXiv, 2025
We present an efficiently computable representation of many-body lattice sums in terms of singular integrals over products of Epstein zeta functions. This method solves a long-standing issue in computing high-dimensional lattice sums to high precision, particularly for three-body interactions like the Axilrod-Teller-Muto (ATM) potential. Our approach significantly reduces computation time and extends to a broad class of n-body lattice sums with linear complexity increase. We demonstrate the method’s efficiency and accuracy, achieving full precision for exponents greater than the system dimension. The paper also includes an application to study the stability of a three-dimensional lattice system with Lennard-Jones two-body interactions under the inclusion of an ATM three-body term at finite pressure.
Recommended citation: Buchheit, A. A., & Busse, J. K. (2025). "Epstein zeta method for many-body lattice sums." arXiv preprint arXiv:2504.11989.
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