Weak universality of the spin glass transition in three dimensions

We perform a finite-size scaling study of the three-dimensional Heisenberg spin glass in the presence of weak random anisotropic interactions, up to lattice sizes $L=32$ . Anisotropies have a major impact on the phase transition. The chiral-glass susceptibility does not diverge due to a large anomalous dimension. It follows that the anisotropic spin glass belongs to a Universality Class different from the isotropic model, which questions the applicability of the chirality scenario.We perform a finite-size scaling study of the three-dimensional Heisenberg spin glass in the presence of weak random anisotropic interactions, up to lattice sizes $L=32$. Anisotropies have a major impact on the phase transition. The chiral-glass susceptibility does not diverge due to a large anomalous dimension. It follows that the anisotropic spin glass belongs to a Universality Class different from the isotropic model, which questions the applicability of the chirality scenario.

arXiv:1101.2509Physical Review BJul 14, 20118 citations

Universality in spin glasses: A Monte Carlo study

Helmut G. Katzgraber, Mathias Körner, A. P. Young

Bulletin of the American Physical SocietyMar 6, 20070 citations

Spin glass behavior in a random Coulomb antiferromagnet

J. Rehn, Roderich Moessner, A. P. Young

We study spin glass behavior in a random Ising Coulomb antiferromagnet in two and three dimensions using Monte Carlo simulations. In two dimensions, we find a transition at zero temperature with critical exponents consistent with those of the Edwards-Anderson model, though with large uncertainties. In three dimensions, evidence for a finite-temperature transition, as occurs in the Edwards-Anderson model, is rather weak. This may indicate that the sizes are too small to probe the asymptotic critical behavior, or possibly that the universality class is different from that of the Edwards-Anderson model and has a lower critical dimension equal to three.We study spin glass behavior in a random Ising Coulomb antiferromagnet in two and three dimensions using Monte Carlo simulations. In two dimensions, we find a transition at zero temperature with critical exponents consistent with those of the Edwards-Anderson model, though with large uncertainties. In three dimensions, evidence for a finite-temperature transition, as occurs in the Edwards-Anderson model, is rather weak. This may indicate that the sizes are too small to probe the asymptotic critical behavior, or possibly that the universality class is different from that of the Edwards-Anderson model and has a lower critical dimension equal to three.

arXiv:1607.04587Physical review. ESep 21, 20165 citations

Nonequilibrium dynamic exponent and spin-glass transitions

Tota Nakamura

Nonequilibrium dynamics of the $\pm J$ Ising, the {\it XY}, and the Heisenberg spin-glass models are investigated in three dimensions. A nonequilibrium dynamic exponent is calculated from the dynamic correlation length. The spin-glass dynamic exponent continuously depends on the temperature. There is no anomaly at the critical temperature as is recently reported by Katzgraber and Campbell. On the other hand, the chiral-glass dynamic exponent takes a constant value above the spin-glass transition temperature ( $T_\mathrm{sg}$ ), and becomes temperature-dependent below $T_\mathrm{sg}$ .The finite-time scaling analyses on the spin- and the chiral-glass susceptibility are performed using the temperature dependence of the dynamic exponent. A difference of the spin- and the chiral-glass transition temperatures is resolved in the Heisenberg model. The dynamic critical exponent takes almost the same value for all transitions. It suggests that the spin-glass and the chiral-glass transitions in three dimensions are dynamically universal.Nonequilibrium dynamics of the $\pm J$ Ising, the {\it XY}, and the Heisenberg spin-glass models are investigated in three dimensions. A nonequilibrium dynamic exponent is calculated from the dynamic correlation length. The spin-glass dynamic exponent continuously depends on the temperature. There is no anomaly at the critical temperature as is recently reported by Katzgraber and Campbell. On the other hand, the chiral-glass dynamic exponent takes a constant value above the spin-glass transition temperature ($T_\mathrm{sg}$), and becomes temperature-dependent below $T_\mathrm{sg}$.The finite-time scaling analyses on the spin- and the chiral-glass susceptibility are performed using the temperature dependence of the dynamic exponent. A difference of the spin- and the chiral-glass transition temperatures is resolved in the Heisenberg model. The dynamic critical exponent takes almost the same value for all transitions. It suggests that the spin-glass and the chiral-glass transitions in three dimensions are dynamically universal.

arXiv:cond-mat/0603062Mar 3, 20060 citations

We perform a finite-size scaling study of the three-dimensional Heisenberg spin glass in the presence of weak random anisotropic interactions, up to lattice sizes

L=32

. Anisotropies have a major impact on the phase transition. The chiral-glass susceptibility does not diverge due to a large anomalous dimension. It follows that the anisotropic spin glass belongs to a Universality Class different from the isotropic model, which questions the applicability of the chirality scenario.

Nonequilibrium dynamics of the

\pm J

Ising, the {\it XY}, and the Heisenberg spin-glass models are investigated in three dimensions. A nonequilibrium dynamic exponent is calculated from the dynamic correlation length. The spin-glass dynamic exponent continuously depends on the temperature. There is no anomaly at the critical temperature as is recently reported by Katzgraber and Campbell. On the other hand, the chiral-glass dynamic exponent takes a constant value above the spin-glass transition temperature (

T_\mathrm{sg}

), and becomes temperature-dependent below

T_\mathrm{sg}

.The finite-time scaling analyses on the spin- and the chiral-glass susceptibility are performed using the temperature dependence of the dynamic exponent. A difference of the spin- and the chiral-glass transition temperatures is resolved in the Heisenberg model. The dynamic critical exponent takes almost the same value for all transitions. It suggests that the spin-glass and the chiral-glass transitions in three dimensions are dynamically universal.