The elastic backbone phase transition in the Ising model

The two-dimensional (zero magnetic field) Ising model is known to undergo a second order para-ferromagnetic phase transition, which is accompanied by a correlated percolation transition for the Fortuin-Kasteleyn (FK) clusters. In this paper we uncover that there exists also a second temperature $T_{\text{eb}}<T_c$ at which the elastic backbone of FK clusters undergoes a second order phase transition to a dense phase. The corresponding universality class, which is characterized by determining various percolation exponents, is shown to be completely different from directed percolation, proposing a new anisotropic universality class with $\beta=0.54\pm 0.02$, $\nu_{||}=1.86\pm 0.01$, $\nu_{\perp}=1.21\pm 0.04$ and $d_f=1.53\pm 0.03$. All tested hyper-scaling relations are shown to be valid.