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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 limit of low temperatures and/or high densities is asymptotically proportional to $rho^{tfrac{p+2}{2}}T^{-tfrac{d}{2}}$ with the particle density $rho$ and the temperature $T$. Dynamic Monte Carlo simulations are performed in 1-, 2- and 3-dimensional systems with different powers $p$, and the results agree with the theoretical predictions.
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 classi
We propose the clock Monte Carlo technique for sampling each successive chain step in constant time. It is built on a recently proposed factorized transition filter and its core features include its O(1) computational complexity and its generality. W
In this article, we present an event-driven algorithm that generalizes the recent hard-sphere event-chain Monte Carlo method without introducing discretizations in time or in space. A factorization of the Metropolis filter and the concept of infinite
We present a method for the direct evaluation of the difference between the free energies of two crystalline structures, of different symmetry. The method rests on a Monte Carlo procedure which allows one to sample along a path, through atomic-displa
In this work, we discuss the implications of a recently obtained equilibrium fluctuation-dissipation relation on the extension of the available Monte Carlo methods based on the consideration of the Gibbs canonical ensemble to account for the existenc