RIGOROUS STUDY OF THE SPIN-1 2 ISING-MODEL IN A LAYERED MAGNETIC-FIELD AT LOW-TEMPERATURES/

We investigate the low-temperature phase diagram of the three-dimensio nal Ising model under an external layered magnetic field, h. For h = 2 we observe that there exists an infinite number of layered ground sta tes and we prove that, at low temperatures, the external Gibbs state ( the 'bilayer' phase) is unique. For h < 2 there exists two ferromagnet ic ground states. Moreover, there exists in the plane (T, h) an open l ine of phase coexistence between the 'bilayer' phase and the '+' and ' -' ferromagnetic phases.