TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.1.030
TI  - Bethe $M$-layer construction for the percolation problem
PY  - 2025/01/23
UR  - https://www.scipost.org/SciPostPhys.18.1.030
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 1
SP  - 030
A1  - Angelini, Maria Chiara
AU  - Palazzi, Saverio
AU  - Rizzo, Tommaso
AU  - Tarzia, Marco
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.18.1.030,
	title={{Bethe $M$-layer construction for the percolation problem}},
	author={Maria Chiara Angelini and Saverio Palazzi and Tommaso Rizzo and Marco Tarzia},
	journal={SciPost Phys.},
	volume={18},
	pages={030},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.1.030},
	url={https://scipost.org/10.21468/SciPostPhys.18.1.030},
}