  We propose and theoretically analyse an experimental configuration in which
lasers induce 3-spin interactions between trapped ions.By properly choosing the
intensities and frequencies of the lasers, 3-spin couplings may be dominant or
comparable to 2-spin terms and magnetic fields. In this way, trapped ions can
be used to study exotic quantum phases which do not have a counterpart in
nature. We study the conditions for the validity of the effective 3-spin
Hamiltonian, and predict qualitatively the quantum phase diagram of the system.
