Quantum phase transitions in XY spin models.

Abstract

The ground state of an $\mathrm{XY}$ model changes at a critical transverse field, above which there is a gap from the fully polarized ground state to the first excitation. We investigate the phase transition from this ``Mott insulator'' phase as the transverse field approaches its critical value. We calculate exactly some Green's functions and critical exponents for $d$-dimensional ferromagnetic lattices and for the Sherrington-Kirkpatrick spin-glass model. Finite-dimensional spin glasses are also discussed.