  A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination
of semi-grandcanonical Monte Carlo (SGMC) and Molecular Dynamics (MD) methods
near a liquid-liquid critical temperature $T_c$. Choosing equal chemical
potentials for the two species, the SGMC switches identities (${\rm A} \to {\rm
B} \to {\rm A}$) to generate well-equilibrated configurations of the system on
the coexistence curve for $T<T_c$ and at the critical concentration, $x_c=1/2$,
for $T>T_c$. A finite-size scaling analysis of the concentration susceptibility
above $T_c$ and of the order parameter below $T_c$ is performed, varying the
number of particles from N=400 to 12800. The data are fully compatible with the
expected critical exponents of the three-dimensional Ising universality class.
  The equilibrium configurations from the SGMC runs are used as initial states
for microcanonical MD runs, from which transport coefficients are extracted.
Self-diffusion coefficients are obtained from the Einstein relation, while the
interdiffusion coefficient and the shear viscosity are estimated from
Green-Kubo expressions. As expected, the self-diffusion constant does not
display a detectable critical anomaly. With appropriate finite-size scaling
analysis, we show that the simulation data for the shear viscosity and the
mutual diffusion constant are quite consistent both with the theoretically
predicted behavior, including the critical exponents and amplitudes, and with
the most accurate experimental evidence.
