  We exploit the Quantum Cluster Variational Method (QCVM) to study the
$J_1$-$J_2$ model for quantum Ising spins. We first describe the QCVM and
discuss how it is related to other Mean Field approximations. The phase diagram
of the model is studied at the level of the Kikuchi approximation in square
lattices as a function of the ratio between $g = J_2/J_1$ , the temperature and
the longitudinal and transverse external fields. Our results show that quantum
fluctuations may change the order of the transition and induce a gap between
the ferromagnetic and the stripe phases. Moreover, when both longitudinal and
transverse fields are present, thermal fluctuations and quantum effects
contribute to the appearance of a nematic phase.
