Related papers: Tuning the generalized Hybrid Monte Carlo algorith…
We present a Monte Carlo method to compute efficiently susceptibilites or covariances of two physical variables. The method relies on a generalization of the exchange cluster algorithm to any model of interacting particles with any $2$-body…
We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of…
Automatic Differentiation (AD) allows to determine exactly the Taylor series of any function truncated at any order. Here we propose to use AD techniques for Monte Carlo data analysis. We discuss how to estimate errors of a general function…
An overview is given over the recently developed and now widely used Monte Carlo algorithms with reduced or eliminated critical slowing down. The basic techniques are overrelaxation, cluster algorithms and multigrid methods. With these…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
We design an enhanced Event-Chain Monte Carlo algorithm to study 1D quantum dissipative systems, using their bosonized representation. Expressing the bosonized Hamiltonian as a path integral over a scalar field enables the application of…
Monte Carlo methods represent a cornerstone of computer science. They allow to sample high dimensional distribution functions in an efficient way. In this paper we consider the extension of Automatic Differentiation (AD) techniques to Monte…
Taking the two-dimensional Ising model for example, short-time behavior of critical dynamics with a conserved order parameter is investigated by Monte Carlo simulations. Scaling behavior is observed, but the dynamic exponent $z$ is updating…
We present cluster Monte Carlo algorithms for the $XYZ$ quantum spin models. In the special case of $S=1/2$, the new algorithm can be viewed as a cluster algorithm for the 8-vertex model. As an example, we study the $S=1/2$ $XY$ model in…
Dynamic relaxation of the XY model quenched from a high temperature state to the critical temperature or below is investigated with Monte Carlo methods. When a non-zero initial magnetization is given, in the short-time regime of the dynamic…
We analyze how the choice of the sampling weight affects the efficiency of the Monte Carlo evaluation of classical time autocorrelation functions. Assuming uncorrelated sampling or sampling with constant correlation length, we propose a…
Using an elaborate set of simulational tools and statistically optimized methods of data analysis we investigate the scaling behavior of the correlation lengths of three-dimensional classical O($n$) spin models. Considering…
Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of general and efficient update algorithm for large size systems close to phase transition or with…
We review the assumptions on which the Monte Carlo renormalization technique is based, in particular the analyticity of the block spin transformations. On this basis, we select an optimized Kadanoff blocking rule in combination with the…
We study the critical behavior of a generalized icosahedral model on the simple cubic lattice. The field variable of the icosahedral model might take one of twelve vectors of unit length, which are given by the normalized vertices of the…
We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where non-local cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase…
We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These bounds require the discretization…
A cluster Monte Carlo algorithm for the Ashkin-Teller (AT) model is constructed according to the guidelines of a general scheme for such algorithms. Its dynamical behaviour is tested for the square lattice AT model. We perform simulations…
We study Monte Carlo calculations of the effective potential for a scalar field theory using three techniques. One of these is a new method proposed and tested for the first time. In each case we extract the renormalised quantities of the…
We review the local Monte Carlo dynamics and Swendsen-Wang cluster algorithm. We introduce and analyze a new Monte Carlo dynamics known as transitional Monte Carlo. The transitional Monte Carlo algorithm samples energy probability…