Elastic backbone phase transition in the Ising model.

Abstract

The two-dimensional (zero magnetic field) Ising model is known to undergo a second-order paraferromagnetic 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_{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, which leads us to propose a new anisotropic universality class with β=0.54±0.02, ν_{||}=1.86±0.01, ν_{⊥}=1.21±0.04, and d_{f}=1.53±0.03. All tested hyperscaling relations are shown to be valid.