Related papers: Numerical simulation study of the dynamical behavi…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
We introduce cluster dynamical models of conflicts in which only the largest cluster can be involved in an action. This mimics the situations in which an attack is planned by a central body, and the largest attack force is used. We study…
We present exact results for a lattice model of cluster growth in 1D. The growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable-phase, +1, regions by overturning the…
We study the dynamic critical behavior of two algorithms: the Swendsen-Wang algorithm for the two-dimensional Potts model with q=2,3,4 and a Swendsen-Wang-type algorithm for the two-dimensional symmetric Ashkin-Teller model on the self-dual…
A comparison between single-cluster and single-spin algorithms is made for the Ising model in 2 and 3 dimensions. We compare the amount of computer time needed to achieve a given level of statistical accuracy, rather than the speed in terms…
On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the…
We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm,…
We perform Monte Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are…
Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…
The cluster algorithm in the fully frustrated Ising model on the square lattice is essentially different from the ones used in other systems. Thus its better understanding is particularly important for finding new lines of development.…
When dissipative particles are left alone, their fluctuation energy decays due to collisional interactions, clusters build up and grow with time until the system size is reached. When the effective dissipation is strong enough, this may…
We construct an efficient cluster algorithm for ferromagnetic SU(N)-symmetric quantum spin systems. Such systems provide a new regularization for CP(N-1) models in the framework of D-theory, which is an alternative non-perturbative approach…
The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based…
The Binder ratios exhibit discrepancy from the Gaussian behavior of the magnetic cumulants, and their size independence at the critical point has been widely utilized in numerical studies of critical phenomena. In the present article we…
We simulate the $N$-spin critical Ising model on a square lattice using Glauber dynamics and consider the typical one-unit time equal to $N$ single-spin-flip attempts. The divergence of correlation time with the linear extent of the system…
Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for post-deposition coarsening dynamics, contains…
An extended polymer collapses to form a globule when subjected to a quench below the collapse transition temperature. The process begins with the formation of clusters of monomers or ``pearls''. The nascent clusters merge, resulting in…
Distributed optimization algorithms are widely used in many industrial machine learning applications. However choosing the appropriate algorithm and cluster size is often difficult for users as the performance and convergence rate of…
A one-dimensional flocking model using active Ising spins is studied, where the system evolves through the reinforcement learning approach \textit{via} defining state, action, and cost function for each spin. The orientation of spin with…
We introduce a novel variance-reducing Monte Carlo algorithm for accurate determination of autocorrelation times. We apply this method to two-dimensional Ising systems with sizes up to $15 \times 15$, using single-spin flip dynamics, random…