Random sampling of self-avoiding theta-graphs

Nicholas R. Beaton; Aleksander L. Owczarek

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arXiv · 2605.04367

Random sampling of self-avoiding theta-graphs

Nicholas R. Beaton·Aleksander L. Owczarek

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Abstract

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.

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Nicholas R. Beaton, Aleksander L. Owczarek. 2026-05-06. Random sampling of self-avoiding theta-graphs. https://arxiv.org/abs/2605.04367

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