Aging in a topological spin glass

We have examined the nonconventional spin glass phase of the 2-dimensional kagome antiferromagnet (H_3 O) Fe_3 (SO_4)_2 (OH)_6 by means of ac and dc magnetic measurements. The frequency dependence of the ac susceptibility peak is characteristic of a critical slowing down at Tg ~ 18K. At fixed temperature below Tg, aging effects are found which obey the same scaling law as in spin glasses or polymers. However, in clear contrast with conventional spin glasses, aging is remarkably insensitive to temperature changes. This particular type of dynamics is discussed in relation with theoretical predictions for highly frustrated non-disordered systems.Comment: 4 pages, 4 figure

Rejuvenation in the Random Energy Model

We show that the Random Energy Model has interesting rejuvenation properties in its frozen phase. Different `susceptibilities' to temperature changes, for the free-energy and for other (`magnetic') observables, can be computed exactly. These susceptibilities diverge at the transition temperature, as (1-T/T_c)^-3 for the free-energy.Comment: 9 pages, 1 eps figur

Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model. II. Quasi-Equilibrium Regime of Spin Auto-Correlation Function

Using Monte Carlo simulations, we have studied isothermal aging of three-dimensional Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation function. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of {\it effective stiffness} for droplet excitations in the presence of domain walls. Within the range of computational time window, we have confirmed that the effective stiffness follows the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls, whose growth law has been extracted from our simulated data. Implication of the results are discussed in relation to experimental works on ac susceptibilities.Comment: 18 pages, 6 figure

Finite-Temperature Transition into a Power-Law Spin Phase with an Extensive Zero-Point Entropy

We introduce an $xy$ generalization of the frustrated Ising model on a triangular lattice. The presence of continuous degrees of freedom stabilizes a {\em finite-temperature} spin state with {\em power-law} discrete spin correlations and an extensive zero-point entropy. In this phase, the unquenched degrees of freedom can be described by a fluctuating surface with logarithmic height correlations. Finite-size Monte Carlo simulations have been used to characterize the exponents of the transition and the dynamics of the low-temperature phase

Fluctuation-dissipation ratio of a spin glass in the aging regime

We present the first experimental determination of the time autocorrelation $C(t',t)$ of magnetization in the non-stationary regime of a spin glass. Quantitative comparison with the response, the magnetic susceptibility $\chi(t',t)$, is made using a new experimental setup allowing both measurements in the same conditions. Clearly, we observe a non-linear fluctuation-dissipation relation between $C$ and $\chi$, depending weakly on the waiting time $t'$. Following theoretical developments on mean-field models, and lately on short range models, it is predicted that in the limit of long times, the $\chi(C)$ relationship should become independent on $t'$. A scaling procedure allows us to extrapolate to the limit of long waiting times.Comment: 4 pages, 3 figure

Chaos and Universality in a Four-Dimensional Spin Glass

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 four seems to be above the critical dimension where chaos with temperature is no more present in the critical region. Our results are consistent with the Gaussian and bimodal coupling distributions being in the same universality class.Comment: 11 pages, including 6 postscript figures. Latex with revtex macro

Temperature shifts in the Sinai model: static and dynamical effects

We study analytically and numerically the role of temperature shifts in the simplest model where the energy landscape is explicitely hierarchical, namely the Sinai model. This model has both attractive features (there are valleys within valleys in a strict self similar sense), but also one important drawback: there is no phase transition so that the model is, in the large size limit, effectively at zero temperature. We compute various static chaos indicators, that are found to be trivial in the large size limit, but exhibit interesting features for finite sizes. Correspondingly, for finite times, some interesting rejuvenation effects, related to the self similar nature of the potential, are observed. Still, the separation of time scales/length scales with temperatures in this model is much weaker that in experimental spin-glasses.Comment: 19 pages, Revtex4, eps figure

Aging, rejuvenation and memory effects in Ising and Heisenberg spin glasses

We have compared aging phenomena in the Fe_{0.5}Mn_{0.5}TiO_3 Ising spin glass and in the CdCr_{1.7}In_{0.3}S_4 Heisenberg-like spin glass by means of low-frequency ac susceptibility measurements. At constant temperature, aging obeys the same `$\omega t$ scaling' in both samples as in other systems. Investigating the effect of temperature variations, we find that the Ising sample exhibits rejuvenation and memory effects which are qualitatively similar to those found in other spin glasses, indicating that the existence of these phenomena does not depend on the dimensionality of the spins. However, systematic temperature cycling experiments on both samples show important quantitative differences. In the Ising sample, the contribution of aging at low temperature to aging at a slightly higher temperature is much larger than expected from thermal slowing down. This is at variance with the behaviour observed until now in other spin glasses, which show the opposite trend of a free-energy barrier growth as the temperature is decreased. We discuss these results in terms of a strongly renormalized microscopic attempt time for thermal activation, and estimate the corresponding values of the barrier exponent $\psi$ introduced in the scaling theories.Comment: 8 pages, including 6 figure

Numerical Study of Aging in the Generalized Random Energy Model

Magnetizations are introduced to the Generalized Random Energy Model (GREM) and numerical simulations on ac susceptibility is made for direct comparison with experiments in glassy materials. Prominent dynamical natures of spin glasses, {\it i.e.}, {\em memory} effect and {\em reinitialization}, are reproduced well in the GREM. The existence of many layers causing continuous transitions is very important for the two natures. Results of experiments in other glassy materials such as polymers, supercooled glycerol and orientational glasses, which are contrast to those in spin glasses, are interpreted well by the Single-layer Random Energy Model.Comment: 8 pages, 9 figures, to be submitted to J. Phys. Soc. Jp

Static chaos and scaling behaviour in the spin-glass phase

We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the magnetic field and their free energy cost is determined by the finite-temperature fixed point exponents. In this framework, numerical results suggest that mean-field chaos exponents are probably exact in finite dimensions. If we use the droplet approach, numerical results suggest that the zero-temperature fixed point exponent $\theta$ is very close to $\frac{d-3}{2}$. In both approaches $d=3$ is the lower critical dimension in agreement with recent numerical simulations.Comment: 28 pages + 6 figures, LateX, figures uuencoded at the end of fil