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Studying Soft Matter with "Soft" Potentials: Fast Lattice Monte Carlo Simulations and Corresponding Lattice Self-Consistent Field Calculations

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.