Related papers: Efficient Monte Carlo Simulation Methods in Statis…
We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct…
A brief introduction to the technique of Monte Carlo simulations in statistical physics is presented. The topics covered include statistical ensembles random and pseudo random numbers, random sampling techniques, importance sampling, Markov…
In any valid Monte Carlo sampling that realizes microcanonical property we can collect statistics for a transition matrix in energy. This matrix is used to determine the density of states, from which most of the thermodynamical averages can…
We discuss a sampling algorithm which generates flat histogram in energy. In combination with transition matrix Monte Carlo, the density of states and derived quantities such as entropy and free energy as a function of temperature can be…
In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…
We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
Monte Carlo computer simulations are virtually the only way to analyze the thermodynamic behavior of a system in a precise way. However, the various existing methods exhibit extreme differences in their efficiency, depending on model…
The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
We analyze a new Monte Carlo method which uses transition matrix in the space of energy. This method gives an efficient reweighting technique. The associated artificial dynamics is a constrained random walk in energy, producing the result…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
A Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum. A random walk in the two-dimensional space of particle number and energy is used to estimate the…