Complexity of Ising spin glasses

We compute the complexity [logarithm of the number of Thouless-Anderson-Palmer (TAP) states] associated with minima and index-one saddle points of the TAP free energy. Higher-index saddles have smaller complexities. The two leading complexities are equal, consistent with the Morse theorem on the total number of turning points, and have the value given by Bray and Moore [J. Phys. C, ()]]. In the thermodynamic limit, TAP states of all free energies become marginally stable.     

On the damage spreading in Ising spin glasses

The spreading of the Hamming distance or damage has been investigated for ±J Ising spin glasses under heat bath dynamics. Dimensions d = 2, 3, 4, 6 and mean field were studied. For finite dimensions, the damage goes to zero at long times above a temperature T_D(d). Accurate values of this critical temperature were obtained, together with certain critical exponents. The spin glass ordering temperatures T_g were also estimated from the damage spreading data. The results are compared with other work and discussed from a phase space approach.     

Free energy fluctuations in Ising spin glasses

The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number n. It is shown that the Parisi symmetry breaking scheme does not give the correct answers for these higher order terms. A modified symmetry breaking scheme with the same stability is shown to resolve the problem.     

Ground-state landscape of J Ising spin glasses

Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40². A combination of a genetic algorithm and Cluster-Exact Approximation is used. For each quenched realization of the bonds up to 40 independent ground states are obtained. For the infinite system a ground-state energy of e =-1.4015(3) is extrapolated. The ground-state landscape is investigated using a finite-size scaling analysis of the distribution of overlaps. The mean-field picture assuming a complex landscape describes the situation better than the droplet-scaling model, where for the infinite system mainly two ground states exist. Strong evidence is found that the ground states are not organized in an ultrametric fashion in contrast to previous results for three-dimensional spin glasses. Received 12 October 1998     

Hidden valley structure of Ising spin glasses

The hidden valley structure of the phase space of short-range spin glasses is investigated. In the spirit of a similar investigation for liquids by Stillinger and Weber, valleys are defined as the set of states which by steepest descent lead to the same metastable state. The lifetime of valleys and the size of spin clusters involved in intervalley transitions on thermal Monte Carlo trajectories are calculated as a function of temperature.     

Temperature and disorder chaos in three-dimensional Ising spin glasses

We study the effects of small temperature as well as disorder perturbations on the equilibrium state of three-dimensional Ising spin glasses via an alternate scaling ansatz. By using Monte Carlo simulations, we show that temperature and disorder perturbations yield chaotic changes in the equilibrium state and that temperature chaos is considerably harder to observe than disorder chaos.     

Size of the critical region in long-range Ising spin glasses

The size of the critical region for long- but not infinite-range Ising spin glasses is calculated by looking at the single loop corrections to the Bethe lattice approximation. The size of the critical region is predicted to go as $\text{1}\text{Z}$ for large Z, where Z is the number of interacting neighbors.     

On the universal behavior of two-dimensional Ising spin glasses

Ising spin glasses are studied, at zero temperature, on a hierarchical lattice as an approach to the square lattice. The stiffness exponent y, which governs the behavior of the interactions under changes of scale, is computed for several distinct continuous symmetric probability distributions for the couplings. All distributions considered lead to the same estimates, i.e., the exponent y is universal. Our results are compared with other estimates available for the two-dimensional Gaussian Ising spin glass.     

Behavior of Ising spin glasses in a magnetic field

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field-temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.     

Aging dynamics of Edwards-Anderson spin glasses

We analyze by means of extensive computer simulations the out of equilibrium dynamics of Edwards-Anderson spin glasses in d = 4 and d = 6 dimensions with ± J interactions. In particular, we focus our analysis on the scaling properties of the two-time autocorrelation function in a wide range of temperatures from T = 0.07 T _c to T = 0.75 T _c in both systems. In both the 4 d and 6 d models at very low temperatures we study the effects of discretization of energy levels. Strong sub-aging behaviors are found. We argue that this is because in the times accessible to our simulations the systems are only able to probe activated dynamics through the lowest discrete energy levels and remain trapped around nearly flat regions of the energy landscape. For temperatures T ≥ 0.5 T _c in 4 d and 6 d we find logarithmic scalings that are compatible with simple dynamical ultrametricity. Nevertheless the behaviour of the systems, even in 6 d is very different from the mean field SK model results. Received 21 October 2002 / Received in final form 13 January 2003 Published online 11 April 2003 RID="a" ID="a"Associate researcher of the Abdus Salam International Centre for Theoretical Physics; e-mail: stariolo@if.ufrgs.br; http://www.if.ufrgs.br/stariolo RID="b" ID="b"Present address: The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy e-mail: mmontemu@ictp.trieste.it RID="c" ID="c"e-mail: tamarit@famaf.unc.edu.ar     

Aging phenomena in spin glasses and frustrated ferromagnets

An experimental protocol developed for spin glasses has been applied to a reentrant system. We compare the main features of the aging phenomena in both spin glass and ferromagnetic phases.     

Strong universality and algebraic scaling in two-dimensional Ising spin glasses

At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but nonzero temperatures and provide numerical evidence that eta approximately equal 0 and nu approximately equal 3.5 in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds, in particular, for the +/- J model, with or without dilutions, and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T = 0, is consistent with a real space renormalization group approach. We also explain how the scaling of the specific heat is compatible with the hyperscaling prediction.     

On the observation of negative magnetization under zero-field-cooled process

We have addressed problems associated with the measurement of zero-field-cooled (ZFC) magnetization and its interpretation in the light of negative magnetization reported in certain ferrimagnetic materials such as CoCr₂O₄. We demonstrate that a small negative trapped field in the sample space as well as large coercive fields are responsible for the observed negative magnetization. The problem is commonly encountered while working with magnetometers and a superconducting magnet where the sign of the trapped field can be positive or negative depending on the way the field is reduced to zero.     

On the dynamic nature of the freezing process in Ising spin glasses

The distribution of local moments in a two dimensional Ising spin glass with short range Gaussian interactions is investigated by Monte Carlo simulations. Below the freezing temperatureT _f , this distribution has a sharp peak at the saturated moment. The spins can clearly be characterized by a fractionq of frozen spins and 1-q of fast spins which are in thermal equilibrium. Just belowT _f the frozen spins appear in small clusters; the spin glass transition isnot a percolation process. Our results support the local and nonequilibrium character of the spin glass transition.q is related to the remanent magnetization (TRM), the linear response and the field cooled susceptibility. As a consequence magnetic resonance experiments should see, in addition to a broad background, a sharp line splitting whose position does not shift with temperature.