When describing many-particle systems, we come across two-body forces all the time - the Coulomb interaction between charged particles, the Lennard-Jones potential, the hard-sphere contact interaction.
However, it is known that there exist three-body potential terms as well (that are not just a sum of 2-body terms). One example is the Axilrod-Teller potential and the exclusion interaction in colloids might have a reasonably relevant three-body term. Also, Wikipedia seems to suggests that three-body forces are necessary to describe systems of nucleons.
Are there any other examples of three-body potentials one might come across in physics? The questions says "useful", because even for the Axilrod-Teller potential, it likely only accounts for a small fraction of the total system energy. It would be nice to have any example where the three-body term is critical for the correct description of the system. (I cannot judge how useful the nucleon three-body force is.)
