# Multiple Walkers in the Wang-Landau Algorithm

## Abstract

The mean cost for converging an estimated density of states using the Wang-Landau algorithm is measured for the Ising and Heisenberg models. The cost increases in a power-law fashion with the number of spins, with an exponent near 3 for one-dimensional models, and closer to 2.4 for two-dimensional models. The effect of multiple, simultaneous walkers on the cost is also measured. For the one-dimensional Ising model the cost can increase with the number of walkers for large systems. For both the Ising and Heisenberg models in two-dimensions, no adverse impact on the cost is observed. Thus multiple walkers is a strategy that should scale well in a parallel computing environment for many models of magnetic materials.

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 885956

- Report Number(s):
- ORNL/TM-2005/1

TRN: US200617%%269

- DOE Contract Number:
- DE-AC05-00OR22725

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; HEISENBERG MODEL; ISING MODEL; MAGNETIC MATERIALS

### Citation Formats

```
Brown, G.
```*Multiple Walkers in the Wang-Landau Algorithm*. United States: N. p., 2005.
Web. doi:10.2172/885956.

```
Brown, G.
```*Multiple Walkers in the Wang-Landau Algorithm*. United States. doi:10.2172/885956.

```
Brown, G. Wed .
"Multiple Walkers in the Wang-Landau Algorithm". United States.
doi:10.2172/885956. https://www.osti.gov/servlets/purl/885956.
```

```
@article{osti_885956,
```

title = {Multiple Walkers in the Wang-Landau Algorithm},

author = {Brown, G},

abstractNote = {The mean cost for converging an estimated density of states using the Wang-Landau algorithm is measured for the Ising and Heisenberg models. The cost increases in a power-law fashion with the number of spins, with an exponent near 3 for one-dimensional models, and closer to 2.4 for two-dimensional models. The effect of multiple, simultaneous walkers on the cost is also measured. For the one-dimensional Ising model the cost can increase with the number of walkers for large systems. For both the Ising and Heisenberg models in two-dimensions, no adverse impact on the cost is observed. Thus multiple walkers is a strategy that should scale well in a parallel computing environment for many models of magnetic materials.},

doi = {10.2172/885956},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Dec 28 00:00:00 EST 2005},

month = {Wed Dec 28 00:00:00 EST 2005}

}

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