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We present a rigorous efficient event-chain Monte Carlo algorithm for long-range interacting particle systems. Using a cell-veto scheme within the factorized Metropolis algorithm, we compute each single-particle move with a fixed number of operations. For slowly decaying potentials such as Coulomb interactions, screening line charges allow us to take into account periodic boundary conditions. We discuss the performance of the cell-veto Monte Carlo algorithm for general inverse-power-law potentials, and illustrate how it provides a new outlook on one of the prominent bottlenecks in large-scale atomistic Monte Carlo simulations.
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We present a novel Ensemble Monte Carlo Growth method to sample the equilibrium thermodynamic properties of random chains. The method is based on the multicanonical technique of computing the density of states in the energy space. Such a quantity is temperature independent, and therefore microcanonical and canonical thermodynamic quantities, including the free energy, entropy, and thermal averages, can be obtained by re-weighting with a Boltzmann factor. The algorithm we present combines two approaches: the first is the Monte Carlo ensemble growth method, where a population of samples in the state space is considered, as opposed to traditional sampling by long random walks, or iterative single-chain growth. The second is the flat-histogram Monte Carlo, similar to the popular Wang-Landau sampling, or to multicanonical chain-growth sampling. We discuss the performance and relative simplicity of the proposed algorithm, and we apply it to known test cases.
We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of cluster algorithms and the treatment of long-range interactions. Dissipative quantum spins and resistively shunted Josephson junctions will be considered.
Ultrathin magnetic films can be modeled as an anisotropic Heisenberg model with long-range dipolar interactions. It is believed that the phase diagram presents three phases: An ordered ferromagnetic phase I, a phase characterized by a change from out-of-plane to in-plane in the magnetization II, and a high-temperature paramagnetic phase III. It is claimed that the border lines from phase I to III and II to III are of second order and from I to II is first order. In the present work we have performed a very careful Monte Carlo simulation of the model. Our results strongly support that the line separating phases II and III is of the BKT type.
The Cooperative Motion Algorithm is an efficient lattice method to simulate dense polymer systems and is often used with two different criteria to generate a Markov chain in the configuration space. While the first method is the well-established Metropolis algorithm, the other one is an heuristic algorithm which needs justification. As an introductory step towards justification for the 3D lattice polymers, we study a simple system which is the binary equimolar uid on a 2D triangular lattice. Since all lattice sites are occupied only selected type of motions are considered, such the vacancy movements, swapping neighboring lattice sites (Kawasaki dynamics) and cooperative loops. We compare both methods, calculating the energy as well as heat capacity as a function of temperature. The critical temperature, which was determined using the Binder cumulant, was the same for all methods with the simulation accuracy and in agreement with the exact critical temperature for the Ising model on the 2D triangular lattice. In order to achieve reliable results at low temperatures we employ the parallel tempering algorithm which enables simultaneous simulations of replicas of the system in a wide range of temperatures.
We introduce an efficient nonreversible Markov chain Monte Carlo algorithm to generate self-avoiding walks with a variable endpoint. In two dimensions, the new algorithm slightly outperforms the two-move nonreversible Berretti-Sokal algorithm introduced by H.~Hu, X.~Chen, and Y.~Deng in cite{old}, while for three-dimensional walks, it is 3--5 times faster. The new algorithm introduces nonreversible Markov chains that obey global balance and allows for three types of elementary moves on the existing self-avoiding walk: shorten, extend or alter conformation without changing the walks length.
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