Finite energy barriers in the random-bond Ising model

One of the last open questions about the existence of a phase transition in the random-bond Ising model refers to the energy barriers between different ground-state valleys concerning a one-spin-flip dynamic (as, e.g., used in Monte Carlo calculations). A barrier of infinite height would imply a symmetry breaking and therefore some kind of phase transition. The present work finds no such barriers by evaluating correlation functions and the ground-state structures of the square-lattice $\pm J$ model.