Critical exponents for a percolation model on transient graphs

We consider the bond percolation problem on a transient weighted graph induced by excursion sets of Gaussian free field corresponding cable system. Owing to continuity this setup and strong Markov property one hand, links with potential theory for associated diffusion other, we rigorously determine behavior various key quantities related (near-)critical regime model. In particular, our results apply in case base is three-dimensional cubic lattice. They unveil values critical exponents, which are explicit but not mean-field consistent predictions from scaling below upper-critical dimension.