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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2025-01-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.1.030 |
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| author | Maria Chiara Angelini, Saverio Palazzi, Tommaso Rizzo, Marco Tarzia |
| author_facet | Maria Chiara Angelini, Saverio Palazzi, Tommaso Rizzo, Marco Tarzia |
| author_sort | Maria Chiara Angelini, Saverio Palazzi, Tommaso Rizzo, Marco Tarzia |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-086edefa245d4b7bb2b46c6ffe01d1c0 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-086edefa245d4b7bb2b46c6ffe01d1c02025-01-23T14:28:19ZengSciPostSciPost Physics2542-46532025-01-0118103010.21468/SciPostPhys.18.1.030Bethe $M$-layer construction for the percolation problemMaria Chiara Angelini, Saverio Palazzi, Tommaso Rizzo, Marco TarziaOne 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.https://scipost.org/SciPostPhys.18.1.030 |
| spellingShingle | Maria Chiara Angelini, Saverio Palazzi, Tommaso Rizzo, Marco Tarzia Bethe $M$-layer construction for the percolation problem SciPost Physics |
| title | Bethe $M$-layer construction for the percolation problem |
| title_full | Bethe $M$-layer construction for the percolation problem |
| title_fullStr | Bethe $M$-layer construction for the percolation problem |
| title_full_unstemmed | Bethe $M$-layer construction for the percolation problem |
| title_short | Bethe $M$-layer construction for the percolation problem |
| title_sort | bethe m layer construction for the percolation problem |
| url | https://scipost.org/SciPostPhys.18.1.030 |
| work_keys_str_mv | AT mariachiaraangelinisaveriopalazzitommasorizzomarcotarzia bethemlayerconstructionforthepercolationproblem |