Two-dimensional periodic frustrated Ising models in a transverse field

We investigate the interplay of classical degeneracy and quantum dynamics i n a range of periodic frustrated transverse field Ising systems at zero tem perature. We find that such dynamics can lead to unusual ordered phases and phase transitions or to a quantum spin liquid (cooperative paramagnetic) p hase as in the triangular and kagome lattice antiferromagnets, respectively . For the latter, we further predict passage to a bond-ordered phase follow ed by a critical phase as the field is tilted. These systems also provide e xact realizations of quantum dimer models introduced in studies of high tem perature superconductivity.