  We study ordering mechanisms which are induced by the quantum fluctuation in
fully frustrated Ising spin systems. Since there are many degenerated states in
frustrated systems, "order by thermal disorder" often takes place due to a kind
of entropy effect. To consider "order by quantum disorder" in fully frustrated
Ising spin systems, we apply transverse field as quantum fluctuation. There
exists a ferromagnetic correlation in each sublattice. The sublattice
correlation at zero temperature is enlarged due to transverse field. The
quantum fluctuation enhances the solid order at zero temperatures. This is an
example of quantum field induced ordering in fully frustrated systems. We also
study a case in which the transverse field induces a reentrant behavior as
another type of order by quantum disorder, and compare correspondent cases in
the classical systems.
