Random-field effect on the quantum ferromagnetic XY model

The quantum version of the random-field spherical XY model on a d-dimensional hypercubic lattice is presented in the boson space, and solved exactly. We recover the Imry-Ma result concerning the lower critical dimension d(c)=4, and calculate the critical exponents near the critical temperature. In particular, we obtain a general phase diagram of the model with arbitrary dimension d when d>d(c). The ferromagnetic ordering is reduced by quantum fluctuations, and destroyed completely by random-field fluctuations with sufficiently large values of the random-field variance sigma. The entropy and the specific heat vanish as T-d/2 at low temperatures. Since the model is equivalent to a Bose system, we show a superfluid-Mott insulator transition at a critical chemical potential mu(c). [S0163-1829(95)00925-4].