  At zero temperature, the classical antiferromagnetic Ising model on the
pyrochlore lattice is a spin disorder phase of the critical spin correlation.
It is a deconfined phase in that the binding energy of the
monopole-anti-monopole pair is independent of their distance of separation. We
show that turning on a transverse magnetic field turns it into the cooperative
paramagnet, and the spin correlation becomes exponential decay. Furthermore, it
introduces the quantum confinement (of magnetic monopoles), where the binding
energy of the pair is proportional to their distance of separation. This
disorder state undergoes adiabatic transition to the paramagnetic state in the
large field limit. The effective Hamiltonian (without magnetic monopoles) in
small field is the Ising Hamiltonian plus ring exchange interaction.
