Related papers: Probability-Changing Cluster Algorithm for Potts M…
We report measurements of the critical exponents of the classical three-dimensional Heisenberg model on simple cubic lattices of size $L^3$ with $L$ = 12, 16, 20, 24, 32, 40, and 48. The data was obtained from a few long single-cluster…
We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a…
In this talk, we briefly comment on Sweeny and Gliozzi methods, cluster Monte Carlo method, and recent transition matrix Monte Carlo for Potts models. We mostly concentrate on a new algorithm known as "binary tree summation". Some of the…
We report the results of simulations of the Lebwohl-Lasher model of the nematic-isotropic transition using a new cluster Monte Carlo algorithm. The algorithm is a modification of the Wolff algorithm for spin systems, and greatly reduces…
We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we…
Recently, Ang--Cai--Sun--Wu (2024) determined the three-point connectivity constant for two-dimensional critical percolation, confirming a prediction of Delfino and Viti (2010). In this paper, we address the analogous problem for planar…
Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical…
We study the O(N) loop model on the Honeycomb lattice with real value $N \geq 1$ by means of a cluster algorithm. The formulation of the algorithm is based on the equivalence of the O(N) loop model and the low-temperature graphical…
We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an…
We present a simple approach to high-accuracy calculations of critical properties for the three-dimensional Ising model, without prior knowledge of the critical temperature. The iterative method uses a modified block-spin transformation…
To identify emerging microscopic structures in low temperature spin glasses, we study self-sustained clusters (SSC) in spin models defined on sparse random graphs. A message-passing algorithm is developed to determine the probability of…
We propose a cluster simulation algorithm for statistical ensembles with fixed order parameter. We use the tethered ensemble, which features Helmholtz's effective potential rather than Gibbs's free energy, and in which canonical averages…
We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well…
The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition…
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…
A cluster Monte Carlo method for systems of classical spins with purely dipolar couplings is presented. It is tested and applied for finite arrays of perpendicular Ising dipoles on the triangular lattice. This model is a modification with…
The invaded cluster approach is extended to 2D Potts model with annealed vacancies by using the random-cluster representation. Geometrical arguments are used to propose the algorithm which converges to the tricritical point in the…
We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts model. We find that the Li-Sokal bound ($\tau_{int,E} \geq const \times C_H$) is…
We present an algorithm which calculates groundstates of Ising spin glasses approximately. It works by randomly selecting clusters of spins which exhibit no frustrations. The spins which were not selected, contribute to the local fields of…
We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster (CC) framework. By combining elements of randomness and determinism, our algorithm achieves a…