After introducing and discussing the link-overlap between spin configurations we show that the Edwards-Anderson model has a replicaequivalent quenched equilibrium state, a property introduced by Parisi in the description of the mean-field spin-glass phase which generalizes ultrametricity. Our method is based on the control of fluctuations through the property of stochastic stability and works f...

Considerable advances have been made in recent years in the understanding of Ising spin glass models in two and three dimensions. Models with continuous degrees-of-freedom, which are often more realistic in describing physical systems, have received much less attention. We study properties of domain-wall excitations in continuous-spin glass systems by means of extensive numerical ground-state c...

We describe the interplay of quantum and thermal fluctuations in the infinite-range Heisenberg spin glass. This model is generalized to SU(N) symmetry, and we describe the phase diagram as a function of the spin S and the temperature T . The model is solved in the large N limit and certain universal critical properties are shown to hold to all orders in 1/N . For large S, the ground state is a ...

After introducing and discussing the link-overlap between spin configurations we show that the Edwards-Anderson model has a replicaequivalent quenched equilibrium state, a precondition for ultrametricity introduced by Parisi in the description of the mean-field spin-glass phase. Our method is based on the control of fluctuations through the property of stochastic stability and works for all the...

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local mag...

After introducing and discussing the link-overlap between spin configurations we show that the Edwards-Anderson model has a replicaequivalent quenched equilibrium state, a property introduced by Parisi in the description of the mean-field spin-glass phase which generalizes ultrametricity. Our method is based on the control of fluctuations through the property of stochastic stability and works f...

The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field D for a large number of spins. This allows us to locate a first-order transition between the spin-glass and paramagnetic phases within a good accuracy. The total number of solutions is also determine...

The concepts of connectivity, localization, and frustration are explored in relation to glass formation in amorphous materials. First, the concept of eigenclusters to geometrically characterize correlations in amorphous materials is introduced, and discussed in detail for both the Ising ferromagnet and Ising spin glass models. Second, a new, glass-forming percolation model that contains frustra...

We use high-temperature and low-concentration series to treat the dilute spin glass within a model with nearest-neighbor interactions which randomly assume the values +J, 0, -J with probabilities p/2, 1-p, p/2, respectively. Using the Harris no-free-end diagrams scheme in general spatial dimension, we obtained 15thorder series for χEA as a function of temperature for arbitrary dilution, 14th-or...