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

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

Dynamical Scaling Analysis for ±J Ising Model in Three Dimensions

Yusuke Terasawa, Yukiyasu Ozeki

The ±J Ising model in three dimensions is investigated using dynamical scaling analysis for a nonequilibrium relaxation process. The spin-glass (SG) transition is analyzed under an assumed dynamical exponent z proposed for the scaling analysis of the SG transition. To estimate dynamical exponent z precisely, we introduce an extrapolation scheme for the asymptotic value of the logarithmic derivative of the dynamical Binder parameter. We obtain the phase diagram in the temperature–concentration (p–T) space, as well as the p-dependence of critical exponents γ, ν, and z. For the static exponents of the SG transition, the universality is strongly indicated numerically along the whole region of the paramagnetic (PM)–SG phase boundary. A remarkable crossover behavior is observed for estimations of critical exponents at the boundary close to the multicritical point (MCP) of PM–ferromagnetic (FM)–SG phases. In addition, the dynamical assumption for z resulting from the slow relaxation in the SG region disappears in the FM region, and the crossover between them occurs around the Nishimori Line.The ±J Ising model in three dimensions is investigated using dynamical scaling analysis for a nonequilibrium relaxation process. The spin-glass (SG) transition is analyzed under an assumed dynamical exponent z proposed for the scaling analysis of the SG transition. To estimate dynamical exponent z precisely, we introduce an extrapolation scheme for the asymptotic value of the logarithmic derivative of the dynamical Binder parameter. We obtain the phase diagram in the temperature–concentration (p–T) space, as well as the p-dependence of critical exponents γ, ν, and z. For the static exponents of the SG transition, the universality is strongly indicated numerically along the whole region of the paramagnetic (PM)–SG phase boundary. A remarkable crossover behavior is observed for estimations of critical exponents at the boundary close to the multicritical point (MCP) of PM–ferromagnetic (FM)–SG phases. In addition, the dynamical assumption for z resulting from the slow relaxation in the SG region disappears in the FM region, and the crossover between them occurs around the Nishimori Line.

Journal of the Physical Society of JapanJun 19, 20234 citations

On the critical dynamics of spin-glasses

Vladimir V. Prudnikov, G. B. Teǐtel'Baum

Physics Letters AMar 1, 19771 citation

Critical Properties of a Simple Spin Glass Model

Amnon Aharony A, Y. Imry

Springer eBooksJan 1, 19770 citations

Finite size scaling study of dynamical phase transitions in two dimensional models : Ferromagnet, symmetric and non symmetric spin glasses

Avidan Uriel Neumann, Bernard Derrida

We study the time evolution of two configurations submitted to the same thermal noise for several two dimensional models (Ising ferromagnet, symmetric spin glass, non symmetric spin glass). For all these models, we find a non zero critical temperature above which the two configurations always meet. Using finite size scaling ideas, we determine for these three models this dynamical phase transition and some of the critical exponents. For the ferromagnet, the transition Tc ≃ 2.25 coincides with the Curie temperature whereas for the two spin glass models ( ± J distribution of bonds) we obtain Tc ≃ 1.5-1.7.We study the time evolution of two configurations submitted to the same thermal noise for several two dimensional models (Ising ferromagnet, symmetric spin glass, non symmetric spin glass). For all these models, we find a non zero critical temperature above which the two configurations always meet. Using finite size scaling ideas, we determine for these three models this dynamical phase transition and some of the critical exponents. For the ferromagnet, the transition Tc ≃ 2.25 coincides with the Curie temperature whereas for the two spin glass models ( ± J distribution of bonds) we obtain Tc ≃ 1.5-1.7.

Journal de physiqueJan 1, 198866 citations

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.