I have been studying molecular dynamics and statistical mechanics, and I have been running into this term called "many-body" forces. I have been reading this paper: https://doi.org/10.1080/01418618808205184. Part 2 of this paper deals with the construction of a new Hamiltonian to describe the potential energies of our system (metallic gold).
They come up with a "glue Hamiltonian" to encompass the many-body forces. From what I understand, these forces arise when 3 or more bodies interact with each other. This is in contrast with the way diatomic potentials work (like gravity, Coulomb, Lennard-Jones, etc.) where two bodies interacting with each other. And for reasons I don't know, the two-body potentials that I am so familiar with, are insufficient to model solids.
My question is, what are these forces? Are they just more... complicated 2-body interactions? What is the motivation to create many-body forces in the first place?