A quantum d-dimensional random-field XY ferromagnet

Ne propose a soluble quantum spherical XY ferromagnet with a random field in the boson space. We obtain a general expression of the critical temperature T-c below which the ordered ferromagnet phase appears. The Imry-Ma result concerning the lower critical dimension d(c) = 4 is recovered, and the critical exponents near the critical temperature T-c are calculated. We show that the random-field fluctuations rather than the quantum fluctuations dominate the phase transition and critical behavior of the system. The entropy vanishes as T-d/2 at low temperatures, contrary to the classical spherical model.