Physical Review Letters

New critical-point exponent and new scaling laws for short-range Ising spin glasses

Muriel Ney‐Nifle, H. J. Hilhorst

Published May 18, 1992• 85 citations

Abstract

We investigate the chaotic temperature dependence of the renormalized couplings in a short-range Ising spin glass. Some of our analytic and numerical results, obtained by the Migdal-Kadanoff renormalization scheme but argued to have general validity, differ from those of the scaling and droplet theory. First, chaos is present also at and above the critical temperature. Second, between ${\mathit{d}}_{\mathit{l}}$=2.46 (the lower critical dimension) and ${\mathit{d}}_{+}$=3.4, the chaos in the critical region is characterized by a new critical exponent ${\mathrm{\ensuremath{\zeta}}}_{\mathit{c}}$ that has hitherto escaped attention.

DOI: 10.1103/physrevlett.68.2992

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Physical Review Letters

New critical-point exponent and new scaling laws for short-range Ising spin glasses

Muriel Ney‐Nifle, H. J. Hilhorst

Published May 18, 1992• 85 citations

Publisher

Abstract

{\mathit{d}}_{\mathit{l}}

=2.46 (the lower critical dimension) and

{\mathit{d}}_{+}

=3.4, the chaos in the critical region is characterized by a new critical exponent

{\mathrm{\ensuremath{\zeta}}}_{\mathit{c}}

that has hitherto escaped attention.

DOI: 10.1103/physrevlett.68.2992

Related papers

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Félix Ritort

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We present a finite-size scaling analysis of Monte Carlo simulation results on a four-dimensional Ising spin-glass. We study chaos with both coupling and temperature perturbations, and find the same chaos exponent in each case. Chaos is investigated both at the critical temperature and below where it seems to be more efficient (larger exponent). Dimension 4 seems to be above the critical dimension where chaos with temperature is no longer present in the critical region. Our results are consistent with the Gaussian and bimodal coupling distributions being in the same universality class.We present a finite-size scaling analysis of Monte Carlo simulation results on a four-dimensional Ising spin-glass. We study chaos with both coupling and temperature perturbations, and find the same chaos exponent in each case. Chaos is investigated both at the critical temperature and below where it seems to be more efficient (larger exponent). Dimension 4 seems to be above the critical dimension where chaos with temperature is no longer present in the critical region. Our results are consistent with the Gaussian and bimodal coupling distributions being in the same universality class.

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

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

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

{\mathit{d}}_{\mathit{l}}

=2.46 (the lower critical dimension) and

{\mathit{d}}_{+}

=3.4, the chaos in the critical region is characterized by a new critical exponent

{\mathrm{\ensuremath{\zeta}}}_{\mathit{c}}

that has hitherto escaped attention.

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.