Related papers: High Precision Simulation Techniques for Lattice F…
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of…
The consideration of quantum fields defined on a spacetime lattice provides computational techniques which are invaluable for studying gauge theories nonperturbatively from first principles. Perturbation theory is an essential aspect of…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
We develop cluster algorithms for a broad class of loop models on two-dimensional lattices, including several standard O(n) loop models at n \ge 1. We show that our algorithm has little or no critical slowing-down when 1 \le n \le 2. We use…
Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped…
How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP)…
We extend a recently proposed real-space renormalization group scheme for dynamical triangulations to situations where the lattice is coupled to continuous scalar fields. Using Monte Carlo simulations in combination with a linear,…
The main idea of this work is that the quantum-classical isomorphism is a suitable framework for a generalization of the notion of detailed balance. The quantum-classical isomorphism is used in order to develop a Monte Carlo simulation with…
We study the relation between the dynamical critical behavior and the kinematics of stochastic multigrid algorithms. The scale dependence of acceptance rates for nonlocal Metropolis updates is analyzed with the help of an approximation…
In Wang-Landau type algorithms, Monte-Carlo updates are performed with respect to the density of states, which is iteratively refined during simulations. The partition function and thermodynamic observables are then obtained by standard…
Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice…
We review the background of the cluster algorithms in Monte Carlo simulation of statistical physics problems. One of the first such successful algorithm was developed by Swendsen and Wang eight years ago. In contrast to the local…
The effectiveness of the recently developed Fixed-Node Quantum Monte Carlo method for lattice fermions, developed by van Leeuwen and co-workers, is tested by applying it to the 1D Kondo lattice, an example of a one-dimensional model with a…
A numerical technique is introduced that reduces exponentially the time required for Monte Carlo simulations of non-equilibrium systems. Results for the quasi-stationary probability distribution in two model systems are compared with the…
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…
Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of…
Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…
We introduce a significant improvement for a relatively new machine learning method called Transformation-Based Learning. By applying a Monte Carlo strategy to randomly sample from the space of rules, rather than exhaustively analyzing all…
The great majority of algorithms employed in the study of lattice field theory are based on Monte Carlo's importance sampling method, i.e. on probability interpretation of the Boltzmann weight. Unfortunately in many theories of interest one…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…