A comprehensive description in all dimensions is provided for the scaling exponent y of low-energy excitations in the Ising spin glass introduced by Edwards and Anderson. A combination of extensive numerical as well as theoretical results suggest that its lower critical dimension is exactly dl=5/2. Such a result would be an essential feature of any complete theory of low-temperature spin glass ...

Facilitated spin models were introduced some decades ago to mimic systems characterized by a glass transition. Recent developments have shown that a class of facilitated spin models is also able to reproduce characteristic signatures of the structural relaxation properties of glass-forming liquids. While the equilibrium phase diagram of these models can be calculated analytically, the dynamics ...

We predict the locations of several multicritical points of the Potts spin glass model on the triangular lattice. In particular, continuous multicritical lines, which consist of multicritical points, are obtained for two types of two-state Potts (i.e., Ising) spin glasses with twoand three-body interactions on the triangular lattice. These results provide us with numerous examples to further ve...

Aging phenomena of short-range Ising spin glass models have been investigated using Monte Carlo simulations. It is found that in the low-temperature spin-glass phase the mean domain size exhibits a crossover from a power-law growth associated with the critical fluctuation at the transition temperature to slower growth inherent in the low-temperature phase. The temperature dependence of the grow...

The spin-glass phase in the LiHoxY1−xF4 compound is considered. At zero transverse field this system is well described by the classical Ising model. At finite transverse field deviations from the transverse field quantum Ising model are significant, and one must take properly into account the hyperfine interactions, the off-diagonal terms in the dipolar interactions, and details of the full J =...

Abstract. We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for which we derive an integral equation in replica symmetric (RS) approximation. A bifurcation analysis of this equation reveals the locations of the ...

LiHoo. ]67Yp.833F4 is a dilute dipolar-coupled Ising magnet with a spin glass transition which can be crossed with temperature T (Ts =0.13 K) or with an effective transverse field I (I s = I K at T=O). The nonlinear susceptibility contains a diverging component which dominates at T=98 mK, but disappears by 25 mK. At the same time, the onset of spin glass behavior in the dissipative linear susce...

Abstract. We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressuretemperature phase diagram, and obtain expressions for the critical boundarie...

We study the zero-temperature critical behavior of the dilute Ising spin glass. In our model nearest-neighbor exchange interactions randomly assume the values +J, 0, -J with probabilities p/2, 1-p, and p/2, respectively. We have generated 15th-order series for the Edwards-Anderson spin-glass susceptibility as a function of concentration p on hypercubic lattices in general dimension. Their analy...

We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of such computationally hard problems to the classical spin glass problems. The quantum spin glass problems arise with the introduction of quantum fluctuations, a...