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We construct asymptotic arguments for the relative efficiency of rejection-free Monte Carlo (MC) methods compared to the standard MC method. We find that the efficiency is proportional to $exp{({const} beta)}$ in the Ising, $sqrt{beta}$ in the classical XY, and $beta$ in the classical Heisenberg spin systems with inverse temperature $beta$, regardless of the dimension. The efficiency in hard particle systems is also obtained, and found to be proportional to $(rhoc -rho)^{-d}$ with the closest packing density $rhoc$, density $rho$, and dimension $d$ of the systems. We construct and implement a rejection-free Monte Carlo method for the hard-disk system. The RFMC has a greater computational efficiency at high densities, and the density dependence of the efficiency is as predicted by our arguments.
We calculate the efficiency of a rejection-free dynamic Monte Carlo method for $d$-dimensional off-lattice homogeneous particles interacting through a repulsive power-law potential $r^{-p}$. Theoretically we find the algorithmic efficiency in the lim
We show how to generalize the Lattice Switch Monte Carlo method to calculate the phase diagram of a binary system. A global coordinate transformation is combined with a modification of particle diameters, enabling the multi-component system in questi
The hard-disk problem, the statics and the dynamics of equal two-dimensional hard spheres in a periodic box, has had a profound influence on statistical and computational physics. Markov-chain Monte Carlo and molecular dynamics were first discussed f
We investigate Monte Carlo simulation strategies for determining the effective (depletion) potential between a pair of hard spheres immersed in a dense sea of much smaller hard spheres. Two routes to the depletion potential are considered. The first
We perform extensive MD simulations of two-dimensional systems of hard disks, focusing on the emph{on}-collision statistical properties. We analyze the distribution functions of velocity, free flight time and free path length for packing fractions ra