Dynamic Monte Carlo method

About: Dynamic Monte Carlo method is a research topic. Over the lifetime, 13294 publications have been published within this topic receiving 371256 citations.

Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited

Abstract: We propose improved versions of the standard diffusion Monte Carlo (DMC) and the lattice regularized diffusion Monte Carlo (LRDMC) algorithms. For the DMC method, we refine a scheme recently devised to treat nonlocal pseudopotential in a variational way. We show that such scheme—when applied to large enough systems—maintains its effectiveness only at correspondingly small enough time-steps, and we present two simple upgrades of the method which guarantee the variational property in a size-consistent manner. For the LRDMC method, which is size-consistent and variational by construction, we enhance the computational efficiency by introducing: (i) an improved definition of the effective lattice Hamiltonian which remains size-consistent and entails a small lattice-space error with a known leading term and (ii) a new randomization method for the positions of the lattice knots which requires a single lattice-space

Noise-induced bistability in a Monte Carlo surface-reaction model

Abstract: We find a noise-induced transition to bistability in a Monte Carlo simulation of a model heterogeneous catalytic chemical reaction which is deterministically monostable. Analysis of the probability density function and the correlation integral of time series of this model indicates the existence and central role of noise in this transition. We find that the behavior of this system is a consequence of the interaction of noise with the spatial degrees of freedom on the model catalytic surface.

A cluster Monte Carlo algorithm for 2-dimensional spin glasses

Abstract: A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional ±J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 1002 down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential ( ξ∼e2βJ) and not as a power law as T↦Tc = 0.

Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces

Abstract: A simple and stable method for computing accurate expectation values of observables with variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC) algorithms is presented. The basic idea consists in replacing the usual “bare” estimator associated with the observable by an improved or “renormalized” estimator. Using this estimator more accurate averages are obtained: Not only the statistical fluctuations are reduced but also the systematic error (bias) associated with the approximate VMC or (fixed-node) DMC probability densities. It is shown that improved estimators obey a zero-variance zero-bias property similar to the usual zero-variance zero-bias property of the energy with the local energy as improved estimator. Using this property improved estimators can be optimized and the resulting accuracy on expectation values may reach the remarkable accuracy obtained for total energies. As an important example, we present the application of our formalism to the computation of forces in molecular systems. Cal...