Related papers: Tuning the generalized Hybrid Monte Carlo algorith…
The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a…
We report on a study of the autocorrelation times of the local version of the Hybrid Monte Carlo (LHMC) algorithm for pure gauge $SU(3)$. We compare LHMC to standard multi-hit Metropolis and to the global version of the same HMC. For every…
We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$.…
We systematically test the performance of several Monte Carlo update schemes for the $(2+1)$d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
We present a way to visualize and quantify renormalization group flows in a space of observables computed using Monte Carlo simulations. We apply the method to classical three-dimensional clock models, i.e., the planar (XY) spin model…
With Monte Carlo methods we investigate the dynamic relaxation of the fully frustrated XY model in two dimensions below or at the Kosterlitz-Thouless phase transition temperature. Special attention is drawn to the sublattice structure of…
The analysis of correlation function data obtained by Monte Carlo simulations of the two-dimensional 4-state Potts model, XY model, and self-dual disordered Ising model at criticality are presented. We study the logarithmic corrections to…
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…
We describe collective-move Monte Carlo algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional Monte Carlo simulations…
We describe a method of Monte-Carlo simulations of simplicial quantum gravity coupled to matter fields. We concentrate mainly on the problem of implementing effectively the random, dynamical triangulation and building in a detailed-balance…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
The time-dependent scaling of the two-time autocorrelation function of spin systems without disorder undergoing phase-ordering kinetics is considered. Its form is shown to be determined by an extension of dynamical scaling to a local…
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…
Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local…
We discuss Monte Carlo dynamics based on <N(sigma, Delta E)>_E, the (microcanonical) average number of potential moves which increase the energy by Delta E in a single spin flip. The microcanonical average can be sampled using Monte Carlo…
Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or…
In this work, we establish $\mathrm{L}^2$-exponential convergence for a broad class of Piecewise Deterministic Markov Processes recently proposed in the context of Markov Process Monte Carlo methods and covering in particular the Randomized…
The improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering is studied. As an indicator for decorrelation the topological charge is used.
We propose a self-adapted Monte Carlo approach to automatically determine the critical temperature by simulating two systems with different sizes at the same temperature. The temperature is increased or decreased by checking the short-time…