Related papers: An introduction to Monte Carlo methods
Monte Carlo algorithms are a foundational pillar of modern computational science, yet their effective application hinges on a deep understanding of their performance trade offs. This paper presents a critical analysis of the evolution of…
A two-dimensional fluid of hard spheres each having a spin $\pm 1$ and interacting via short-range Ising-like interaction is studied near the second order phase transition from the paramagnetic gas to the ferromagnetic gas phase. Monte…
Monte Carlo simulation provides a powerful tool for understanding and exploring thermodynamic phase equilibria in many-particle interacting systems. Among the most physically intuitive simulation methods is Gibbs ensemble Monte Carlo…
Computational experiments are used to show that grain boundary mobility is independent of driving force in a two-dimensional, square-lattice Ising model with Metropolis kinetics. This is established over the entire Monte Carlo temperature…
Algorithms to determine transition probabilities in Monte Carlo simulations are tested using a system of classical particles with effective interactions which reproduce Bose-Einstein statistics. The system is appropriate for testing…
The Coherent Ising Machine (CIM) is a quantum network of optical parametric oscillators (OPOs) intended to find ground states of the Ising model. This is an NP-hard problem, related to several important minimization problems, including the…
We present a method for Monte Carlo sampling on systems with discrete variables (focusing in the Ising case), introducing a prior on the candidate moves in a Metropolis-Hastings scheme which can significantly reduce the rejection rate,…
Monte Carlo simulation studies are at the core of the modern applied, computational, and theoretical statistical literature. Simulation is a broadly applicable research tool, used to collect data on the relative performance of methods or…
We present the numerical results for low temperature behavior of the transverse-field Ising model on a frustrated checkerboard lattice, with focus on the effect of both quantum and thermal fluctuations. Applying the recently-developed…
The population annealing algorithm is a population-based equilibrium version of simulated annealing. It can sample thermodynamic systems with rough free-energy landscapes more efficiently than standard Markov chain Monte Carlo alone. A…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
A Monte Carlo Renormalization Group algorithm is used on the Ising model to derive critical exponents and the critical temperature. The algorithm is based on a minimum relative entropy iteration developed previously to derive potentials…
Acceptance-rejection (AR), Independent Metropolis Hastings (IMH) or importance sampling (IS) Monte Carlo (MC) simulation algorithms all involve computing ratios of probability density functions (pdfs). On the other hand, classifiers…
We calculate the critical temperature of the Ising model on a set of graphs representing a concatenated three-bit error-correction code. The graphs are derived from the stabilizer formalism used in quantum error correction. The stabilizer…
With the developed "extended Monte Calro" (EMC) algorithm, we have studied the depinning transition in Ising-type lattice models by extensive numerical simulations, taking the random-field Ising model with a driving field and the driven…
We present computer simulations of a dynamic Monte Carlo algorithm for polymer chains on the FCC lattice which takes explicitly into account the possibility to overcome topological constraints by controlling the rate at which nearby polymer…
A new Monte Carlo algorithm is introduced for the simulation of supercooled liquids and glass formers, and tested in two model glasses. The algorithm is shown to thermalize well below the Mode Coupling temperature and to outperform other…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and beyond that is found to deal well with systems with complex free-energy landscapes. Above all else, it promises…
We apply extensive Monte Carlo simulations to study the probability distribution $P(m)$ of the order parameter $m$ for the simple cubic Ising model with periodic boundary condition at the transition point. Sampling is performed with the…