Bethe $M$-layer construction for the percolation problem
One way to perform field theory computations for the bond percolation problem is through the Kasteleyn and Fortuin mapping to the $n+1$ states Potts model in the limit of $n \to 0$. In this paper, we show that it is possible to recover the $\epsilon$-expansion for critical exponents in finite dimens...
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| Format: | Article |
| Language: | English |
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SciPost
2025-01-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.1.030 |
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| Summary: | One way to perform field theory computations for the bond percolation problem is through the Kasteleyn and Fortuin mapping to the $n+1$ states Potts model in the limit of $n \to 0$. In this paper, we show that it is possible to recover the $\epsilon$-expansion for critical exponents in finite dimension directly using the $M$-layer expansion, without the need to perform any analytical continuation. Moreover, we also show explicitly that the critical exponents for site and bond percolation are the same. This computation provides a reference for applications of the $M$-layer method to systems where the underlying field theory is unknown or disputed. |
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| ISSN: | 2542-4653 |