Empirical relations between static and dynamic exponents for Ising model cluster algorithms

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 of site updates per second or the dynamical critical exponents. Our main result is that the cluster algorithms become more efficient when the system size, Ld, exceeds, L~70–300 for d=2 and l~80–200 for d=3. The exact value of the crossover is dependent upon the computer being used. The lower end of the crossover range is typical of workstations while the higher end is typical of vector computers. Hence, even for workstations, the system sizes needed for efficient use of the cluster algorithm is relatively large.

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CRITICAL DYNAMICS OF TWO-REPLICA CLUSTER ALGORITHMS

International Journal of Modern Physics C ◽

10.1142/s0129183101001663 ◽

2001 ◽

Vol 12 (02) ◽

pp. 257-271

Author(s):

X.-N. LI ◽

J. MACHTA

Keyword(s):

Ising Model ◽

Critical Behavior ◽

Cluster Algorithm ◽

The Other ◽

Square Lattice ◽

Critical Dynamics ◽

Two Dimensional ◽

Cluster Algorithms ◽

Dynamic Exponent

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.

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Critical dynamics of cluster algorithms in the dilute Ising model

Journal of Statistical Physics ◽

10.1007/bf01048034 ◽

1993 ◽

Vol 72 (3-4) ◽

pp. 829-844 ◽

Cited By ~ 9

Author(s):

M. Hennecke ◽

U. Heyken

Keyword(s):

Ising Model ◽

Critical Dynamics ◽

Cluster Algorithms ◽

Dilute Ising Model

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Transition matrix cluster algorithms

International Journal of Modern Physics C ◽

10.1142/s0129183119500049 ◽

2019 ◽

Vol 30 (01) ◽

pp. 1950004 ◽

Cited By ~ 1

Author(s):

David Yevick ◽

Yong Hwan Lee

Keyword(s):

Ising Model ◽

Density Of States ◽

Matrix Method ◽

Transition Matrix ◽

Detailed Balance ◽

Accurate Method ◽

Single Spin ◽

Cluster Algorithms ◽

Global Cluster ◽

Model Transition

We demonstrate that a series of procedures for increasing the efficiency of transition matrix calculations can be realized by integrating the standard single-spin flip transition matrix method with global cluster flipping techniques. Our calculations employ a simple and accurate method based on detailed balance for computing the density of states from the Ising model transition matrix.

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