  The dynamic and static critical behavior of five binary Lennard-Jones liquid
mixtures, close to their continuous demixing points (belonging to the so-called
model H' dynamic universality class), are studied computationally by combining
semi-grand canonical Monte Carlo simulations and large-scale molecular dynamics
(MD) simulations, accelerated by graphic processing units (GPU). The symmetric
binary liquid mixtures considered cover a variety of densities, a wide range of
compressibilities, and various interactions between the unlike particles. The
static quantities studied here encompass the bulk phase diagram (including both
the binodal and the $\lambda$-line), the correlation length, the concentration
susceptibility, the compressibility of the finite-sized systems at the bulk
critical temperature $T_c$, and the pressure. Concerning the collective
transport properties, we focus on the Onsager coefficient and the shear
viscosity. The critical power-law singularities of these quantities are
analyzed in the mixed phase (above $T_c$) and non-universal critical amplitudes
are extracted. Two universal amplitude ratios are calculated. The first one
involves static amplitudes only and agrees well with the expectations for the
three-dimensional Ising universality class. The second ratio includes also
dynamic critical amplitudes and is related to the Einstein--Kawasaki relation
for the interdiffusion constant. Precise estimates of this amplitude ratio are
difficult to obtain from MD simulations, but within the error bars our results
are compatible with theoretical predictions and experimental values for model
H'. Evidence is reported for an inverse proportionality of the pressure and the
isothermal compressibility at the demixing transition, upon varying either the
number density or the repulsion strength between unlike particles.
