  Finite-size effects in systems with diverging characteristic lengthscale have
been addressed via state-of-the-art Monte Carlo and molecular dynamics
simulations of various models exhibiting solid-solid, liquid-liquid and
vapor-liquid transitions. Our simulations, combined with the appropriate
application of finite-size scaling theory, confirm various non-trivial
singularities in equilibrium dynamic critical phenomena and non-equilibrium
domain coarsening phenomena, as predicted by analytical theories. We
convincingly demonstrate that the finite-size effects in the domain growth
problems, with conserved order parameter dynamics, is weak and universal,
irrespective of the transport mechanism. This result is strikingly different
from the corresponding effects in critical dynamics. In critical phenomena,
difference in finite-size effects between statics and dynamics is also
discussed.
