Related papers: Monte Carlo Sampling in Fractal Landscapes
We investigate a generic, parallel replica-exchange framework for Monte Carlo simulations based on the Wang-Landau method. To demonstrate its advantages and general applicability for massively parallel simulations of complex systems, we…
Monte Carlo simulation has been performed in one-dimensional Lebwohl-Lasher model and two dimensional XY-model using the Wang-Landau and the Wang-Landau-Transition-Matrix Monte Carlo methods. Random walk has been performed in the…
We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models. The density of states is modified at each step when the energy…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
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…
We introduce a parallel Wang-Landau method based on the replica-exchange framework for Monte Carlo simulations. To demonstrate its advantages and general applicability for simulations of complex systems, we apply it to different spin models…
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…
While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the…
We report a new multicanonical Monte Carlo (MC) algorithm to obtain the density of states (DOS) for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain an analytical form for the DOS…
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random…
In chaotic dynamical systems, a number of rare trajectories with low level of chaoticity are embedded in chaotic sea, while extraordinary unstable trajectories can exist even in weakly chaotic regions. In this study, a quantitative method…
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…
The sampling of the configuration space in diffusion Monte Carlo (DMC) is done using walkers moving randomly. In a previous work on the Hubbard model [\href{https://doi.org/10.1103/PhysRevB.60.2299}{Assaraf et al.~Phys.~Rev.~B \textbf{60},…
When performing a Monte Carlo calculation, the running time should in principle be much longer than the autocorrelation time in order to get reliable results. Among different lattice fermion models, the Holstein model is notorious for its…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…
The diagrammatic Monte Carlo (Diag-MC) method is a numerical technique which samples the entire diagrammatic series of the Green's function in quantum many-body systems. In this work, we incorporate the flat histogram principle in the…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
Estimating characteristics of large graphs via sampling is a vital part of the study of complex networks. Current sampling methods such as (independent) random vertex and random walks are useful but have drawbacks. Random vertex sampling…
Monte Carlo integration is a powerful tool for scientific and statistical computation, but faces significant challenges when the integrand is a multi-modal distribution, even when the mode locations are known. This work introduces novel…