Finite-size scaling of the Domain Wall Entropy for the 2D \pm J Ising Spin Glass
Abstract
Description
The statistics of domain walls for ground states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 20$, and $x$ = 0.25 and 0.5, where $x$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. Under these conditions, almost all domain walls have an energy $E_{dw}$ equal to 0 or 4. The probability distribution of the entropy, $S_{dw}$, is found to depend strongly on $E_{dw}$. The results for $S_{dw}$ when $E_{dw} = 4$ agree with the prediction of the droplet model. Our results for $S_{dw}$ when $E_{dw} = 0$ agree with those of Saul and Kardar. In addition, we find that the distributions do not appear to be Gaussian in that case. The special role of $E_{dw} = 0$ domain walls is discussed, and the discrepancy between the prediction of Amoruso, Hartmann, Hastings and Moore and the result of Saul and Kardar is explained.
Six pages, extensively revised, submitted to PRB
Six pages, extensively revised, submitted to PRB