ORNSTEIN-ZERNIKE DECAY IN THE GROUND-STATE OF THE QUANTUM ISING-MODEL IN A STRONG TRANSVERSE FIELD

We consider the quantum mechanical Ising ferromagnet in a strong transverse magnetic field in any number of dimensions, d. We prove that in the ground state the power law correction to the exponential decay of the two point function is d/2. The proof begins by writing the ground state as a classical system in one more dimension. (Thus the classical Ornstein-Zernike power of (d - 1)/2 becomes d/2). We then develop a convergent polymer expansion and use the techniques of Bricmont and Frohlich [5].