Relaxation behavior of fractal-cluster spin glasses

2013

Y para que conste, cumplimiento de la legislación vigente, informan favorablemente sobre la referida Tesis Doctoral y autorizan su presentación para su admisión a trámite. Zaragoza, a 29 de abril de 2013 Los directores de la Tesis

World Journal of Condensed Matter Physics, 2012

The dissipative part of the linear magnetic dynamic susceptibility of dipolar spin glasses is considered. Due to the transition of the system (at enough high concentration of the magnetic dipoles) from a paramagnetic phase to magnetic dipolar one, an anomalous temperature dependence of the dissipative part of the magnetic susceptibility is found. Our results are in qualitative agreement with experiments performed on the dipolar-coupled Ising magnet LiHo x Y 1-x F 4 .

Fractals, 2003

We consider a frustrated spin model with a glassy dynamics characterized by a slow component and a fast component in the relaxation process. The slow process involves variables with critical behavior at finite temperature T p and has a global character like the (structural) α-relaxation of glasses. The fast process has a more local character and can be associated to the β-relaxation of glasses. At temperature T > T p the fast relaxation follows the non-Arrhenius behavior of the slow variables. At T T p the fast variables have an Arrhenius behavior, resembling the α − β bifurcation of fragile glasses. The model allows us to analyze the relation between the dynamics and the thermodynamics.

Journal of Physics A: Mathematical and General, 1999

We study the properties of the q-state frustrated bond percolation model by a Monte Carlo "bond flip" dynamics, using an algorithm originally devised by Sweeny and suitably modified to treat the presence of frustration. For q = 2 the model gives the cluster formulation of the Edwards Anderson spin glass. We analyze the percolation transition of the model, and find that it falls in the universality class of the q/2-state ferromagnetic Potts model. We then investigate the bond flip dynamics of the model, and find that, while for temperatures higher than the percolation transition Tp the relaxation functions are fitted by a single exponential, for T < Tp they show a two step decay, reminiscent of the relaxation of glass forming liquids. The long time decay (α-relaxation) is well fitted for T < Tp by a stretched exponential function, showing that in this model the relevant mechanism for the appearing of stretched exponentials is the percolation transition. At very low temperatures the relaxation functions develop a long plateau, as observed in glass forming liquids.

New Journal of Physics, 2010

Reversion of thermoremanent magnetization decay is observed in a canonical spin glass; that is, the system is remagnetized despite the absence of a magnetic field. This unexpected phenomenon occurs only when the system is heated or cooled back to the temperature T 0 at which it was previously subjected to a magnetic field for a significant length of time. Therefore, this reversion can be interpreted as a restoration of the spin state existing before at T 0 . This new information will be a key to resolving a long-standing controversy regarding the nature of spin glasses.

Physical Review B, 2012

We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at zero temperature upon small changes in the magnetic field. For the infinite-range Sherrington-Kirkpatrick model we present a detailed derivation of the density ρ(∆M) of the magnetization jumps ∆M. It is obtained by introducing a multi-component generalization of the Parisi-Duplantier equation, which allows us to compute all cumulants of the magnetization. We find that ρ(∆M) ∼ ∆M −τ with an avalanche exponent τ = 1 for the SK model, originating from the marginal stability (criticality) of the model. It holds for jumps of size 1 ∆M < N 1/2 being provoked by changes of the external field by δH = O(N −1/2) where N is the total number of spins. Our general formula also suggests that the density of overlap q between initial and final state in an avalanche is ρ(q) ∼ 1/(1 − q). These results show interesting similarities with numerical simulations for the out-ofequilibrium dynamics of the SK model. For finite-range models, using droplet arguments, we obtain the prediction τ = (d f +θ)/dm where d f , dm and θ are the fractal dimension, magnetization exponent and energy exponent of a droplet, respectively. This formula is expected to apply to other glassy disordered systems, such as the random-field model and pinned interfaces. We make suggestions for further numerical investigations, as well as experimental studies of the Barkhausen noise in spin glasses.

Complex Behaviour of …, 1997

Journal of Statistical Physics, 2009

Using the dedicated computer Janus, we follow the nonequilibrium dynamics of the Ising spin glass in three dimensions for eleven orders of magnitude. The use of integral estimators for the coherence and correlation lengths allows us to study dynamic heterogeneities and the presence of a replicon mode and to obtain safe bounds on the Edwards-Anderson order parameter below the critical temperature. We obtain good agreement with experimental determinations of the temperature-dependent decay exponents for the thermoremanent magnetization. This magnitude is observed to scale with the much harder to measure coherence length, a potentially useful result for experimentalists. The exponents for energy relaxation display a linear dependence on temperature and reasonable extrapolations to the critical point. We conclude examining the time growth of the coherence length, with a comparison of critical and activated dynamics.

Physical Review B, 1984

We have studied the critical behavior of a purely relaxational dynamic model for Ising spins with quenched random exchange. In zero magnetic field we find a nontrivial stable fixed point below six dimensions in agreement with previous static calculations. It is shown, to lowest order in a=6d, that van Hove theory correctly predicts the dynamic exponent z=2(2g). I. INTROjDUCTION The critical behavior as well as the low-temperature phase of magnetic systems with quenched random exchange continues to attract intensive research. ' Most theoretical work has concentrated on a spin-glass (SG) model introduced by Edwards and Anderson (EA), or rather its long-range version as proposed by Sherrington and Kirkpatrick, to provide a realization of the meanfield (MF) liinit of the short-range model. Whereas the physical interpretation of the MF results for the lowtemperature phase are still controversial, the predictions of MF theory for T) T, are generally accepted. Within MF theory the transition is second order, signaled by a divergence of the static uniform order-parameter susceptibility and a divergence of the relaxation rate of the dynamic spin autocorrelation. The first attempt to go beyond MF theory was undertaken by Harris, t.ubensky, and Chen. These authors studied the static critical behavior in zero field using the renormalization group (RG). A nontrivial fixed point was found in an expansion around the upper critical dimensionality and critical exponents were calculated in an expansion in @=6d. Subsequently, Bray and Roberts' extended the work of Ref. 4 to finite fields in order to study the critical behavior along the de Almeida-Thouless line. Surprisingly they were unable to locate a stable fixed point below six dimensioris. Another surprising result was obtained by Chen and Lubensky, who considered a model with competing ferromagnetic and antiferromagnetic ordering. They found complex exponents for XY' and Heisenberg spins at the ferromagneticspin-glass multicritical point. Neither of these results appears to be understood. All of these calculations made use of the replica trick. Even though it is generally believed that above T, no problems arise with replica symmetry breaking, it is not yet clear whether this is true only within MF theory or also in the more general case, that is, when fluctuations are important.

Physical Review B, 2002