Scaling properties of the damage cloud in the 3D Ising model

The authors show that in the three-dimensional Ising model at the critical temperature the fractal dimension of the touching damage, determined by the box counting method, asymptotically converges to the expected value d f =d- beta /v. In contrast, the finite-size scaling analysis indicates for the touching damage an effective fractal dimension whose value is 20% smaller. The expected d f is, however, recovered again when instead of the system size L the quantity L/ln L is used as a scaling variable. This behaviour could be explained by the recently discovered dynamical multiscaling.