Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D $\pm J$ Ising Spin Glass

Abstract

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 $L\le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. When $L$ is even, almost all domain walls have energy $E_{dw}$ = 0 or 4. When $L$ is odd, most domain walls have $E_{dw}$ = 2. The probability distribution of the entropy, $S_{dw}$, is found to depend strongly on $E_{dw}$. When $E_{dw}=0$, the probability distribution of $|S_{dw}|$ is approximately exponential. The variance of this distribution is proportional to $L$, in agreement with the results of Saul and Kardar. For $E_{dw}=k>0$ the distribution of $S_{dw}$ is not symmetric about zero. In these cases the variance still appears to be linear in $L$, but the average of $S_{dw}$ grows faster than $\sqrt{L}$. This suggests a one-parameter scaling form for the $L$-dependence of the distributions of $S_{dw}$ for $k>0$.

13 pages

References in corpus (2)

• Correlation length of the two-dimensional Ising spin glass with bimodal interactions
• Energy size effects of two-dimensional Ising spin glasses

Cited by in corpus (7)

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• Subextensive singularity in the 2D $\pm J$ Ising spin glass
• Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D $\pm J$ Random-Bond Ising Model
• Aspect-Ratio Scaling of Domain Wall Entropy for the 2D $\pm J$ Ising Spin Glass
• Domain wall entropy of the bimodal two-dimensional Ising spin glass