Random sampling of self-avoiding theta-graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915983618211840 |
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| author | Beaton, Nicholas R. Owczarek, Aleksander L. |
| author_facet | Beaton, Nicholas R. Owczarek, Aleksander L. |
| contents | Theta-graphs are a type of spatial graph with two vertices connected by three edges. We investigate embeddings of theta-graphs in the square and simple cubic lattices, using a combination of the Wang-Landau Monte Carlo method with a variant of the BFACF algorithm which accommodates vertices of degree 3. This allows us to estimate the critical exponents governing the number of theta-graphs and the distributions of the different arm-lengths. For the cubic lattice these values can be compared to the corresponding exponents for prime knots. We also study the number of `monodisperse' theta-graphs where the three arms have the same lengths, and find evidence supporting a conjecture for the critical exponent in two dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04367 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Random sampling of self-avoiding theta-graphs Beaton, Nicholas R. Owczarek, Aleksander L. Statistical Mechanics Soft Condensed Matter 82B41, 82D60, 82M31, 65C05 Theta-graphs are a type of spatial graph with two vertices connected by three edges. We investigate embeddings of theta-graphs in the square and simple cubic lattices, using a combination of the Wang-Landau Monte Carlo method with a variant of the BFACF algorithm which accommodates vertices of degree 3. This allows us to estimate the critical exponents governing the number of theta-graphs and the distributions of the different arm-lengths. For the cubic lattice these values can be compared to the corresponding exponents for prime knots. We also study the number of `monodisperse' theta-graphs where the three arms have the same lengths, and find evidence supporting a conjecture for the critical exponent in two dimensions. |
| title | Random sampling of self-avoiding theta-graphs |
| topic | Statistical Mechanics Soft Condensed Matter 82B41, 82D60, 82M31, 65C05 |
| url | https://arxiv.org/abs/2605.04367 |