  We study the quantum Ising model in D dimensions with the equation of motion
technique, in combination with the Majorana representation for spins. The
decoupling scheme used for the Green's functions is based on the hierarchy of
correlations in position space. To lowest order this method reproduces the well
known mean field phase diagram and critical exponents. When correlations
between spins are included, we show how the appearance of thermal fluctuations
and magnons strongly affect the physical properties. We demonstrate that in 1D
and for B=0, thermal fluctuations completely destroy the ordered phase, and
that near the quantum critical point, the quantum model displays different
behavior than its classical counterpart. We discuss the connection with the
Dyson's equation formalism and the explicit form of the self-energies.
