Bethe $M$-layer construction for the percolation problem - Maria Chiara Angelini, Saverio Palazzi, Tommaso Rizzo, Marco Tarzia (SciPost Physics)
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 $n → 0$. In this paper, we show that it is possible to recover the $ε$-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.