Domain-wall free energy $\ensuremath{\delta}F$, entropy $\ensuremath{\delta}S$, and the correlation function ${C}_{\mathrm{temp}}$ of $\ensuremath{\delta}F$ are measured independently in the four-dimensional $\ifmmode\pm\else\textpm\fi{}J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $\ensuremath{\theta}$, the fractal dimension of domain walls ${d}_{s}$ , and the chaos exponent $\ensuremath{\zeta}$ are extracted from the finite-size scaling analysis of $\ensuremath{\delta}F$, $\ensuremath{\delta}S$, and ${C}_{\mathrm{temp}}$ , respectively, well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation $\ensuremath{\zeta}={d}_{s}/2\ensuremath{-}\ensuremath{\theta}$ 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 $\ensuremath{\delta}F$, entropy $\ensuremath{\delta}S$, and the correlation function ${C}_{\mathrm{temp}}$ of $\ensuremath{\delta}F$ are measured independently in the four-dimensional $\ifmmode\pm\else\textpm\fi{}J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $\ensuremath{\theta}$, the fractal dimension of domain walls ${d}_{s}$, and the chaos exponent $\ensuremath{\zeta}$ are extracted from the finite-size scaling analysis of $\ensuremath{\delta}F$, $\ensuremath{\delta}S$, and ${C}_{\mathrm{temp}}$, respectively, well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation $\ensuremath{\zeta}={d}_{s}/2\ensuremath{-}\ensuremath{\theta}$ 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.

arXiv:cond-mat/0411138Physical Review LettersDec 20, 200544 citations

Chaotic Size Dependence in Spin Glasses

Charles M. Newman, Daniel L. Stein

Springer eBooksJan 1, 19937 citations

Temperature Chaos and Bond Chaos in the Edwards-Anderson Ising Spin Glass : Domain-Wall Free-Energy Measurements

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

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

The spin-glass transition: exponents and dynamics

L. Bernardi, Ney Lemke, Pierre‐Olivier Mari +3 more

arXiv:cond-mat/9804244Physica A Statistical Mechanics and its ApplicationsAug 1, 19985 citations

Domain-wall free energy $\ensuremath{\delta}F$, entropy $\ensuremath{\delta}S$, and the correlation function

{C}_{\mathrm{temp}}

of $\ensuremath{\delta}F$ are measured independently in the four-dimensional $\ifmmode\pm\else\textpm\fi{}J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $\ensuremath{\theta}$, the fractal dimension of domain walls

{d}_{s}

, and the chaos exponent $\ensuremath{\zeta}$ are extracted from the finite-size scaling analysis of $\ensuremath{\delta}F$, $\ensuremath{\delta}S$, and

{C}_{\mathrm{temp}}

, respectively, well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation $\ensuremath{\zeta}={d}_{s}/2\ensuremath{-}\ensuremath{\theta}$ 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.