Related papers: Highly optimized simulations on single- and multi-…
In this report we give an overview on recent results obtained from extensive Monte Carlo (MC) computer simulations of the 3D 2-state (Ising) and 4-state Potts models with bond-dilution. The motivation to study the 4-state Potts model…
We show that addition of Metropolis single spin-flips to the Wolff cluster flipping Monte Carlo procedure leads to a dramatic {\bf increase} in performance for the spin-1/2 Ising model. We also show that adding Wolff cluster flipping to the…
A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum…
We present a parallel machine, based on programmable devices, dedicated to simulate spin glass models with Z2 variables and short range interaction. A working prototype is described for two lattices containing 312x312 spins each with an…
We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted such that a broad distribution of the Parisi overlap parameter $q$ is achieved. Canonical expectation values for…
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 the results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass with Gaussian disorder. Using parallel tempering (replica exchange) Monte Carlo we measure various static, as…
Monte Carlo simulations are widely employed to measure the physical properties of glass-forming liquids in thermal equilibrium. Combined with local Monte Carlo moves, the Metropolis algorithm can also be used to simulate the relaxation…
Monte Carlo simulation using the standard single-spin flip algorithm often fails to sample over the entire configuration space at low temperatures for frustrated spin systems. A typical example is a class of spin-ice type Ising models. In…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
We present a numerical study of an Ising spin glass with hierarchical interactions - the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF)…
Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment on our paper the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling…
Recently, spatial photonic Ising machines (SPIMs) have demonstrated the abilities to compute the Ising Hamiltonian of large-scale spin systems, with the advantages of ultrafast speed and high power efficiency. However, such optical…
This paper introduces novel method of simulation of lipid biomembranes based on Metropolis Hastings algorithm and Graphic Processing Unit computational power. Method gives up to 55 times computational boost in comparison to classical…
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 study the three-dimensional (3D) bond-diluted Edwards-Anderson (EA) model with binary interactions at a bond occupation of 45% by Monte Carlo (MC) simulations. Using an efficient cluster MC algorithm we are able to determine the…
Ising machines are effective solvers for complex combinatorial optimization problems. The idea is mapping the optimal solution(s) to a combinatorial optimization problem to the minimum energy state(s) of a physical system, which naturally…
The Metropolis-Hastings algorithm is a fundamental Markov chain Monte Carlo (MCMC) method for sampling and inference. With the advent of Big Data, distributed and parallel variants of MCMC methods are attracting increased attention. In this…
Brute-force simulations for dynamics on very large networks are quite expensive. While phenomenological treatments may capture some macroscopic properties, they often ignore important microscopic details. Fortunately, one may be only…
Magnetohydrodynamic (MHD) simulations based on the ideal MHD equations have become a powerful tool for modeling phenomena in a wide range of applications including laboratory, astrophysical, and space plasmas. In general, high-resolution…