Related papers: A comparative study of selected parallel tempering…
In this paper, we present a parallel algorithm for Monte Carlo simulation of the 2D Ising Model to perform efficiently on a cluster computer using MPI. We use C++ programming language to implement the algorithm. In our algorithm, every…
We proposed the method that translates the 2-D CSP for minimizing the number of cuts to the Ising model. After that, we conducted computer experiments of the proposed model using the benchmark problem. From the above, the following results…
Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity…
Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel…
Algorithms for simulating complex physical systems or solving difficult optimization problems often resort to an annealing process. Rather than simulating the system at the temperature of interest, an annealing algorithm starts at a…
Error-mitigation methods for Ising machines are reexamined not merely as noise-suppression techniques but as a structural design problem of replica-coupled Ising models. Using simulated annealing as a hardware-noise-free testbed, we…
A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution…
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform…
Developing efficient MCMC algorithms is indispensable in Bayesian inference. In parallel tempering, multiple interacting MCMC chains run to more efficiently explore the state space and improve performance. The multiple chains advance…
While gradient-based discrete samplers are effective in sampling from complex distributions, they are susceptible to getting trapped in local minima, particularly in high-dimensional, multimodal discrete distributions, owing to the…
Recently a cluster Monte Carlo algorithm has been used very successfully in the two-dimensional Edwards-Anderson (EA) model. We show that this algorithm and a variant thereof can also be used successfully in models with a non-zero spin…
Although many efficient heuristics have been developed to solve binary optimization problems, these typically produce correlated solutions for degenerate problems. Most notably, transverse-field quantum annealing - the heuristic employed in…
Combinatorial optimization algorithms which compute exact ground state configurations in disordered magnets are seen to exhibit critical slowing down at zero temperature phase transitions. Using arguments based on the physical picture of…
We use Monte Carlo (MC) methods to simulate a two-dimensional (2D) bond-diluted Ising model on the square lattice which has frustration between the nearest-neighbor interaction J1 and the next-nearest-neighbor interaction J2. In this paper,…
We have introduced a variational method to improve the computation of integrated correlation times in the Parallel Tempering Dynamics, obtaining a better estimate (a lower bound, at least) of the exponential correlation time. Using this…
We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal function that depends on the average statistical fluctuations of the potential and on the…
The multicanonical method has been proven powerful for statistical investigations of lattice and off-lattice systems throughout the last two decades. We discuss an intuitive but very efficient parallel implementation of this algorithm and…
We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo…
We discuss methods that allow to increase the step-size in a parallel tempering simulation of statistical models and test them at the example of the three-dimensional Heisenberg spin glass. We find an overall speed-up of about two for…
We apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature $T=0$ of the two-dimensional Ising model with random $J= \pm 1$ couplings. Analyzing the…