Aspect-Ratio Scaling of the Domain-Wall Energy for the 2D $\pm J$ Random-Bond Ising ModelAspect-Ratio Scaling of the Domain-Wall Energy for the 2D $\pm J$ Random-Bond Ising Model

Ronald Fisch, Alexander K. Hartmann

Mar 27, 20060 citations

Finite-Size Scaling in the Energy-Entropy Plane for the 2D ± Ising Spin Glass

Ronald Fisch

arXiv:cond-mat/0502605Journal of Statistical PhysicsJul 25, 20062 citations

Temperature Chaos and Bond Chaos in the Four-Dimensional $\pm$ J Ising Spin Glass : Domain-Wall Free-Energy MeasurementsTemperature Chaos and Bond Chaos in the Four-Dimensional $\pm$J Ising Spin Glass : Domain-Wall Free-Energy Measurements

M. Sasaki, Koji Hukushima, Hajime Yoshino +1 more

Nov 5, 20040 citations

Finite-size scaling of the Domain Wall Entropy for the 2D \pm J Ising Spin Glass

Ronald Fisch

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.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.

arXiv:cond-mat/0508468Aug 19, 20050 citations

Stiffness exponent of two-dimensional Ising spin glasses for nonperiodic boundary conditions using aspect-ratio scaling

Alexander K. Hartmann, Alan J. Bray, Adam C. Carter +2 more

We study the scaling behavior of domain-wall energies in two-dimensional Ising spin glasses with Gaussian and bimodal distributions of the interactions and different types of boundary conditions. The domain walls are generated by changing the boundary conditions at $T=0$ in one direction. The ground states of the original and perturbed system are calculated numerically by applying an efficient matching algorithm. Systems of size $L\ifmmode\times\else\texttimes\fi{}M$ with different aspect-ratios $1/8<~L/M<~64$ are considered. For Gaussian interactions, using the aspect-ratio scaling approach, we find a stiffness exponent $\ensuremath{\theta}=\ensuremath{-}0.287(4),$ which is independent of the boundary conditions in contrast to earlier results. Furthermore, we find a scaling behavior of the domain-wall energy as predicted by the aspect-ratio approach. Finally, we show that this approach does not work for the bimodal distribution of interactions.We study the scaling behavior of domain-wall energies in two-dimensional Ising spin glasses with Gaussian and bimodal distributions of the interactions and different types of boundary conditions. The domain walls are generated by changing the boundary conditions at $T=0$ in one direction. The ground states of the original and perturbed system are calculated numerically by applying an efficient matching algorithm. Systems of size $L\ifmmode\times\else\texttimes\fi{}M$ with different aspect-ratios $1/8<~L/M<~64$ are considered. For Gaussian interactions, using the aspect-ratio scaling approach, we find a stiffness exponent $\ensuremath{\theta}=\ensuremath{-}0.287(4),$ which is independent of the boundary conditions in contrast to earlier results. Furthermore, we find a scaling behavior of the domain-wall energy as predicted by the aspect-ratio approach. Finally, we show that this approach does not work for the bimodal distribution of interactions.

arXiv:cond-mat/0208546Physical review. B, Condensed matterDec 4, 200252 citations

Dynamic scaling in the two-dimensional Ising spin glasses

Na Xu, Kai-Hsin Wu, Shanon J. Rubin +2 more

Bulletin of the American Physical SocietyMar 5, 20180 citations

Aspect-Ratio Scaling of the Domain-Wall Energy for the 2D

\pm J

Random-Bond Ising Model

Temperature Chaos and Bond Chaos in the Four-Dimensional

\pm

J Ising Spin Glass : Domain-Wall Free-Energy Measurements

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.

T=0

in one direction. The ground states of the original and perturbed system are calculated numerically by applying an efficient matching algorithm. Systems of size $L\ifmmode\times\else\texttimes\fi{}M$ with different aspect-ratios

1/8<~L/M<~64

are considered. For Gaussian interactions, using the aspect-ratio scaling approach, we find a stiffness exponent $\ensuremath{\theta}=\ensuremath{-}0.287(4),$ which is independent of the boundary conditions in contrast to earlier results. Furthermore, we find a scaling behavior of the domain-wall energy as predicted by the aspect-ratio approach. Finally, we show that this approach does not work for the bimodal distribution of interactions.