  The random transverse-field Ising ferromagnet (RTFIF) is a highly disordered
quantum system which contains randomness in the coupling strengths as well as
in the transverse-field strengths. In one dimension, the critical properties
are governed by an infinite-randomness fixed point (IRFP), and
renormalization-group studies argue that the two-dimensional (2D) model is also
governed by an IRFP. However, even the location of the critical point remains
unsettled among quantum Monte Carlo (QMC) studies. In this work, we perform
extensive QMC simulations to locate the quantum critical point and attempt a
finite-size scaling analysis to observe the critical behavior. We estimate the
critical field strength of the 2D RTFIF as $\Gamma_c = 7.52(2)$, together with
critical exponents such as $\beta=1.5(3)$, $\nu = 1.6(3)$, and $z=3.3(3)$ or
$\psi=0.50(3)$. We have also considered the McCoy-Wu model, which has
randomness in the ferromagnetic coupling strengths but not in the
transverse-field strength. Our QMC calculation shows that the critical behavior
of the 2D McCoy-Wu model is closer to that of the 2D transverse-field Ising
spin glass than to that of the 2D RTFIF. These numerical findings enhance our
understanding of disordered 2D quantum systems.
