  The basic idea of fast Monte Carlo (MC) simulations is to perform
particle-based MC simulations with the excluded-volume interactions modeled by
"soft" repulsive potentials that allow particle overlapping. This gives much
faster system relaxation and better sampling of the configurational space than
conventional molecular simulations with "hard" repulsions that prevent particle
overlapping. Here we present fast lattice MC (FLMC) simulations for confined
homopolymers, where multiple occupancy of lattice sites is allowed with a
proper Boltzmann weight and thus the evaluation of nearest-neighbor
interactions can also be avoided. When compared with the corresponding lattice
field theories based on the \emph{same} Hamiltonian, FLMC simulations further
provide a powerful means for unambiguously and quantitatively revealing the
correlation/fluctuation effects.
