Crack Roughness in the 2D Random Threshold Beam Model

We study the scaling of two-dimensional crack roughness using large scale beam lattice systems. Our results indicate that the crack roughness obtained using beam lattice systems does not exhibit anomalous scaling in sharp contrast to the simulation results obtained using scalar fuse lattices. The local and global roughness exponents ($\zeta_{loc}$ and $\zeta$, respectively) are equal to each other, and the two-dimensional crack roughness exponent is estimated to be $\zeta_{loc} = \zeta = 0.64 \pm 0.02$. Removal of overhangs (jumps) in the crack profiles eliminates even the minute differences between the local and global roughness exponents. Furthermore, removing these jumps in the crack profile completely eliminates the multiscaling observed in other studies. We find that the probability density distribution $p(\Delta h(\ell))$ of the height differences $\Delta h(\ell) = [h(x+\ell) - h(x)]$ of the crack profile obtained after removing the jumps in the profiles follows a Gaussian distribution even for small window sizes ($\ell$).