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

Domain-wall free-energy $\delta F$ , entropy $\delta S$ , and the correlation function, $C_{\rm temp}$ , of $\delta F$ are measured independently in the four-dimensional $\pm J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $\theta$ , the fractal dimension of domain walls $d_{\rm s}$ and the chaos exponent $\zeta$ are extracted from the finite-size scaling analysis of $\delta F$ , $\delta S$ and $C_{\rm temp}$ respectively well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation $\zeta=d_{\rm s}/2-\theta$ derived by the droplet theory within our numerical accuracy. We also study bond chaos induced by random variation of bonds, and find that the bond and temperature perturbations yield the universal chaos effects described by a common scaling function and the chaos exponent. These results strongly support the appropriateness of the droplet theory for the description of chaos effect in the EA Ising spin glasses.Domain-wall free-energy $\delta F$, entropy $\delta S$, and the correlation function, $C_{\rm temp}$, of $\delta F$ are measured independently in the four-dimensional $\pm J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $\theta$, the fractal dimension of domain walls $d_{\rm s}$ and the chaos exponent $\zeta$ are extracted from the finite-size scaling analysis of $\delta F$, $\delta S$ and $C_{\rm temp}$ respectively well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation $\zeta=d_{\rm s}/2-\theta$ derived by the droplet theory within our numerical accuracy. We also study bond chaos induced by random variation of bonds, and find that the bond and temperature perturbations yield the universal chaos effects described by a common scaling function and the chaos exponent. These results strongly support the appropriateness of the droplet theory for the description of chaos effect in the EA Ising spin glasses.

Jan 1, 20050 citations

Low temperature behavior of the two-dimensional Ising spin glass

L. W. Lee, Helmut G. Katzgraber, A. P. Young

APSMar 1, 20040 citations

Numerical and experimental studies of the dynamics of Ising spin glasses

Jan‐Olov Andersson

Jan 1, 19941 citation

Fragility of the Equilibrium State in the Four-Dimensional ±JIsing Spin Glass

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

Domain-wall free-energy, the difference in the free-energy between the system with the periodic boundary condition (BC) and that with the anti-periodic BC, is measured in the 4 dimensional ±J Ising spin glass. Temperature dependence of the domain-wall free-energy for each sample shows that the favorable BC changes with temperature, suggesting the existence of temperature chaos. We also investigate fragility of the equilibrium state against small changes of couplings { Jij } (bond chaos) by measuring the domain-wall free-energy. As a result, we find scaling behavior which suggests that the chaos exponent and the scaling function for temperature perturbation are the same as those for bond perturbation, meaning that temperature chaos and bond chaos belong to the same universarity class on fragility.Domain-wall free-energy, the difference in the free-energy between the system with the periodic boundary condition (BC) and that with the anti-periodic BC, is measured in the 4 dimensional ±J Ising spin glass. Temperature dependence of the domain-wall free-energy for each sample shows that the favorable BC changes with temperature, suggesting the existence of temperature chaos. We also investigate fragility of the equilibrium state against small changes of couplings { Jij } (bond chaos) by measuring the domain-wall free-energy. As a result, we find scaling behavior which suggests that the chaos exponent and the scaling function for temperature perturbation are the same as those for bond perturbation, meaning that temperature chaos and bond chaos belong to the same universarity class on fragility.

Progress of Theoretical Physics SupplementJan 1, 20050 citations

Non-Equilibrium Relaxation Study of Ising Spin Glass Models

之康尾関, Yukiyasu Ozeki

Jan 1, 20010 citations

Temperature Chaos and Bond Chaos in the Four-Dimensional

\pm

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

Domain-wall free-energy

\delta F

, entropy

\delta S

, and the correlation function,

C_{\rm temp}

, of

\delta F

are measured independently in the four-dimensional

\pm J

Edwards-Anderson (EA) Ising spin glass. The stiffness exponent

\theta

, the fractal dimension of domain walls

d_{\rm s}

and the chaos exponent

\zeta

are extracted from the finite-size scaling analysis of

\delta F

\delta S

and

C_{\rm temp}

respectively well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation

\zeta=d_{\rm s}/2-\theta

derived by the droplet theory within our numerical accuracy. We also study bond chaos induced by random variation of bonds, and find that the bond and temperature perturbations yield the universal chaos effects described by a common scaling function and the chaos exponent. These results strongly support the appropriateness of the droplet theory for the description of chaos effect in the EA Ising spin glasses.