# Automatic contraction of unstructured tensor networks

## Abstract

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local.

- Authors:

- Flatiron Institute

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1591698

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Published Article

- Journal Name:
- SciPost Physics Proceedings

- Additional Journal Information:
- Journal Name: SciPost Physics Proceedings Journal Volume: 8 Journal Issue: 1; Journal ID: ISSN 2542-4653

- Publisher:
- Stichting SciPost

- Country of Publication:
- Netherlands

- Language:
- English

### Citation Formats

```
Jermyn, Adam. Automatic contraction of unstructured tensor networks. Netherlands: N. p., 2020.
Web. doi:10.21468/SciPostPhys.8.1.005.
```

```
Jermyn, Adam. Automatic contraction of unstructured tensor networks. Netherlands. doi:10.21468/SciPostPhys.8.1.005.
```

```
Jermyn, Adam. Wed .
"Automatic contraction of unstructured tensor networks". Netherlands. doi:10.21468/SciPostPhys.8.1.005.
```

```
@article{osti_1591698,
```

title = {Automatic contraction of unstructured tensor networks},

author = {Jermyn, Adam},

abstractNote = {The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local.},

doi = {10.21468/SciPostPhys.8.1.005},

journal = {SciPost Physics Proceedings},

number = 1,

volume = 8,

place = {Netherlands},

year = {2020},

month = {1}

}

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DOI: 10.21468/SciPostPhys.8.1.005

DOI: 10.21468/SciPostPhys.8.1.005

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