We implement the Stoner model, a textbook Hamiltonian for itinerant ferromagnetism,
using a two-component gas of free fermions with short-range repulsive interactions, which can
capture the essence of the screened Coulomb interaction in electron gases. However, there
is no proof so far that this simple model for ferromagnetism is consistent when the strong
interactions are treated beyond mean-field approaches. It is known that this model fails in one
dimension where the ground state is singlet for arbitrary interactions, or for two particles in
any dimension. Here, cold atoms are used to perform a quantum simulation of this model
Hamiltonian in 3D and show experimentally that it leads to a ferromagnetic phase transition.

An important recent development in cold atom science has been the realization of superfluidity
and the BEC-BCS crossover in strongly interacting two-component Fermi gases near a
Feshbach resonance. These phenomena occur for attractive interactions for negative scattering
length and for bound molecules (corresponding to a positive scattering length for two
unpaired atoms). Very little attention has been given to the region for atoms with strongly
repulsive interactions. One reason is that this region is an excited branch, which is unstable
against near-resonant three-body recombination into weakly-bound molecules. Nevertheless,
many theoretical papers have proposed a two-component Fermi gas near a Feshbach resonance
as a model system for itinerant ferromagnetism assuming that the decay into molecules
can be sufficiently suppressed.