  Solving intractable mathematical problems in simulators composed of atoms,
ions, photons or electrons has recently emerged as a subject of intense
interest. Here we extend this concept to phonons that are localised in
spectrally pure resonances in an electromechanical system which enables their
interactions to be exquisitely fashioned via electrical means. We harness this
platform to emulate the Ising Hamiltonian whose spin 1/2 particles are
replicated by the phase bistable vibrations from a parametric resonance where
multiple resonances play the role of a spin bath. The coupling between the
mechanical pseudo spins is created by generating thermomechanical two-mode
squeezed states which impart correlations between resonances that can imitate a
ferromagnetic, random or an anti-ferromagnetic state on demand. These results
suggest an electromechanical simulator for the Ising Hamiltonian could be built
with a large number of spins with multiple degrees of coupling, a task that
would overwhelm a conventional computer.
