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

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dc.creatorFisch, Ronald
dc.date2006-08-21
dc.date.accessioned2026-07-07T07:41:48Z
dc.date.available2026-07-07T07:41:48Z
dc.descriptionThe 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 $k > 0$.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/cond-mat/0608460
dc.identifierhttp://arxiv.org/abs/cond-mat/0608460
dc.identifierJ. Stat. Phys. 125, 793 (2006)
dc.identifierdoi:10.1007/s10955-006-9223-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122249
dc.subjectStatistical Mechanics
dc.titleFinite-Size Scaling of the Domain Wall Entropy Distributions for the 2D $\pm J$ Ising Spin Glass
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