Wolff Cluster Algorithm Research Articles

Wolff algorithm and anisotropic continuous-spin models: An application to the spin-van der Waals model.

The problem of applying Wolff's cluster algorithm to anisotropic classical spin models is resolved by modifying a part of the Wolff algorithm. To test the effectiveness of our modified algorithm, the spin--van der Waals model is investigated in detail. Our estimate of the dynamical exponent of the model is z=0.19\ifmmode\pm\else\textpm\fi{}0.04.

Multiple Potts models coupled to two-dimensional quantum gravity

We perform Monte Carlo simulations using the Wolff cluster algorithm of multiple q=2, 3, 4 state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the c>1 region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for c>1. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for c>1.

A NUMERICAL TEST OF KPZ SCALING: POTTS MODELS COUPLED TO TWO-DIMENSIONAL QUANTUM GRAVITY

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 in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3, 4 where no exact solution is available. Using Binder’s cumulant we find that the q=10 Potts model displays a first order phase transition on a dynamical graph, as it does on a fixed lattice. We also examine the internal geometry of the graphs generated in the simulation, finding a linear relationship between ring length probabilities and the central charge of the Potts model.

A study of symmetry restoration at finite temperature in the O(4) model using anisotropic lattices

Results of investigations of the O(4) spin model at finite temperature using anisotropic lattices are presented. In both the large N approximation and the numerical simulations using the Wolff cluster algorithm we find that the ratio of the symmetry restoration temperature T SR to the Higgs mass m H is independent of the anisotropy. We obtain a lower bound of 0.59 ± 0.04 for the ratio, T SR /m H , at m H ⋍ 0.5 , which is lowered furhter by about 10% at m H a ⋍ 1 .

Potts models coupled to two-dimensional quantum gravity

Abstract We perform Monte Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3 and 4 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3,4 where no exact solution is available.

ISING MODEL SIMULATIONS ON THE MANIFOLDS OF TWO-DIMENSIONAL QUANTUM GRAVITY

The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical random triangulation, there is no analytical prediction for the quenched case, since these manifolds do not have internal Hausdorff dimension and the problem cannot be formulated in matrix model language. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to ten thousand triangles. The Metropolis algorithm was used for the spin update in order to obtain the initial estimation of the Curie point. After that we used the Wolff cluster algorithm in the critical region. We observed a second order phase transition, similar to that for the Ising model on a regular 2-dimensional lattice, and measured the critical exponents.

A new MCRG calculation of the critical behavior of the 3d Ising model

We have undertaken a large-scale computer simulation of the 3d Ising model using the Monte Carlo Renormalization Group (MCRG) method. Our calculation improves on past calculations in three ways. Firstly, many more operators - 53 even spin and 46 odd spin - are measured. Secondly, larger lattices are used. Lastly, we are incorporating more efficient methods of spin update (Wolff's cluster algorithm). We are aiming to collect at least one hundered thousand measurements at two temperatures on two lattice sizes - 64 3 and 128 3. Currently we have finished the runs for the first temperature and are about half-way through those for the second. Here we present results for the first temperature.

Finite-temperature symmetry restoration in the four-dimensional q4 model with four components

The finite-temperature symmetry restoration in the four-dimensional θ 4 theory with four components and with an infinite self-coupling is studied by means of Monte Carlo simulations on lattices with time extensions L t = 4,5,6 and space extensions 12 3−28 3. The numerical calculations are done by means of the Wolff cluster algorithm which is very efficient for simulations near a phase transition. The numerical results are in goof agreement with an improved one-loop expansion and with the 1/ N-expansion, indicating that in the electroweak theory the symmetry restoration temperature T sr is about 350 GeV.