arXiv:physics/0007091 · International Journal of Modern Physics C

CRITICAL DYNAMICS OF TWO-REPLICA CLUSTER ALGORITHMS

X.-N. LI, Jonathan L. Machta

Published Feb 1, 2001• 2 citations

Abstract

The dynamic critical behavior of the two-replica cluster algorithm is studied. Several versions of the algorithm are applied to the two-dimensional, square lattice Ising model with a staggered field. The dynamic exponent for the full algorithm is found to be less than 0.4. It is found that odd translations of one replica with respect to the other together with global flips are essential for obtaining a small value of the dynamic exponent.

DOI: 10.1142/s0129183101001663

Related papers

Graphical representations and cluster algorithms for critical points with fields

Oliver Redner, Jonathan L. Machta, L. Chayes

A two-replica graphical representation and associated cluster algorithm are described that are applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are associated with the percolation threshold of the graphical representation. Results from numerical simulations of the Ising model in a staggered field are presented. For this case, the dynamic exponent for the algorithm is measured to be less than 0.5.

arXiv:cond-mat/9802063Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsSep 1, 199830 citations

Numerical simulation study of the dynamical behavior of the Niedermayer algorithm

Daniel Girardi, N. S. Branco

We calculate the dynamic critical exponent for the Niedermayer algorithm applied to the two-dimensional Ising and XY models, for various values of the free parameter E 0 . For E 0 = − 1 we regain the Metropolis algorithm and for E 0 = 1 we regain the Wolff algorithm. For − 1 < E 0 < 1, we show that the mean size of the clusters of (possibly) turned spins initially grows with the linear size of the lattice, L , but eventually saturates at a given lattice size , which depends on E 0 . For , the Niedermayer algorithm is equivalent to the Metropolis one, i.e., they have the same dynamic exponent. For E 0 > 1, the autocorrelation time is always greater than for E 0 = 1 (Wolff) and, more important, it also grows faster than a power of L . Therefore, we show that the best choice of cluster algorithm is the Wolff one, when comparing against the Niedermayer generalization. We also obtain the dynamic behavior of the Wolff algorithm: although not conclusively, we propose a scaling law for the dependence of the autocorrelation time on L .

arXiv:1003.3655Journal of Statistical Mechanics Theory and ExperimentApr 16, 20102 citations

CRITICAL DYNAMICS OF THE ISING MODEL WITH ISING MACHINE

N. Ito, Makoto Taiji, Masuo Suzuki

The dynamical critical exponent z of he two-dimensional Ising model with sequential-flip heat-bath dynamics is numerically estimated to be 2.2, which agrees with that of Metropolis dynamics. The dedicated machine "m-TIS", designed and constructed by the present authors is used for the simulations.

Le Journal de Physique ColloquesDec 1, 19882 citations

Single-cluster Monte Carlo study of the Ising model on two-dimensional random lattices

Wolfhard Janke E, Mohammad W. Katoot, Ramon Villanova

We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices with up to 80 000 sites which are linked together according to the Voronoi-Delaunay prescription. In one set of simulations we use reweighting techniques and finite-size scaling analysis to investigate the critical properties of the model in the very vicinity of the phase transition. In the other set of simulations we study the approach to criticality in the disordered phase, making use of improved estimators for measurements. From both sets of simulations we obtain clear evidence that the critical exponents agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model.

arXiv:hep-lat/9402008Physical review. B, Condensed matterApr 1, 199460 citations

HIGH SPEED ALGORITHMS AND SIMULATIONS OF THE CRITICAL DYNAMICS OF THE ISING MODEL

Hans-Otto Heuer

We review the development of Monte Carlo algorithms for the simulation of the Ising model with local dynamics. The multi lattice coding algorithm for the pure and for the site-disordered Ising model is described in detail. Application of these algorithms on fast vector computers have led to new progress concerning the critical dynamics of the pure Ising model leading to the critical exponent z = 2:05. The importance of disorder for the critical dynamics of the Ising model has been investigated recently. We review the numerical results and compare with theoretical predictions. A crossover scenario is found as for the static behavior with an effective dynamical exponent z = 1:75 fl. 1 Introduction The Ising model is a standard model in statistical physics for the description of a ferromagnet in an extremely simplified manner. It is assumed that quantum spin operators may be replaced by classical spins S i = \\Sigma 1 which are oriented parallel or antiparallel to a magnetic filed H: H...

WORLD SCIENTIFIC eBooksMay 1, 19961 citation

Cluster Monte Carlo and network flow algorithms for critical phenomena

Ilija Dukovski

Phase transitions and critical phenomena in several spin models are studied. These models include a two and three dimensional XY model and Ising models in structured and random field. The methods of study are cluster Monte Carlo simulations and network flow optimization algorithms. The XY model and a related soft spin model belonging to the O(2) universality class are studied using a modified version of the Invaded Cluster algorithm. The static critical properties of the models and the dynamic characteristics of the algorithm are studied. The critical exponent η for the O(2) universality class in two and three dimensions is measured. The Invaded Cluster algorithm for the XY model does not show any critical slowing for global variables. Benzene adsorption in a nanoporous solid is modeled with an Ising model with both internal and external magnetic fields. The first order phase transition and the critical properties of the system are studied. The system is simulated using the two replica cluster algorithm. The critical temperature of the system is found to decrease with increasing difference of the values of the internal fields. It is found that the system undergoes a phase transition for a relatively wide, experimentally obtainable, region of values of its parameters. The random field Ising model in three dimensions is studied at zero temperature. The nature of randomness induced phase transition is studied using a numerical network flow optimization method. It is found that the latent heat at the phase transition vanishes in the limit of infinite system size which can be taken as a proof of a second order phase transition.

Jan 1, 20010 citations