Identities and inequalities are proved for the derivatives of order parameters and correlation functions of the Ising spin glass along a line in the phase diagram. The results serve as additional evidence that the ferromagnetic phase is composed of two regions, one with strong ferromagnetic ordering and the other with the effects of disorder dominant. The Nishimori line marks a crossover betwee...

The low-field susceptibility along the easy axis of the spin glass Fe2Ti05 exhibits a sharp cusp at Tg = 48 K, whereas the susceptibility in transverse directions exhibits a broad maximum around 6 K. In all directions irreversibility appears already. below Tz. Transverse irreversibility, however, is weaker by an order of magnitude than the longitudinal one. This behavior is discussed in terms o...

We consider the q-state Potts spin-glass model, with quenched couplings taking two different values only. As an approximation for this model a proper generalization of the random energy model is derived. Formulas of the resulting diluted generalized random energy model (DGREM) are applied to calculate the ground-state energy for the two-dimensional Potts spin-glass model. The semianalytical res...

We consider a finite-range spin glass model in arbitrary dimension, where the strength of the two-body coupling decays to zero over some distance gamma(-1). We show that, under mild assumptions on the interaction potential, the infinite-volume free energy of the system converges to that of the Sherrington-Kirkpatrick one, in the Kac limit gamma-->0. This could be a first step toward an expansio...

The mean-field theory of a spin glass with a specific form of nearestand next-nearest-neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we find either the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one-step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations ...

2014 We study a spin glass model on a hierarchical lattice in the limit in which the number of rungs, p at each stage of the hierarchy tends to infinity. In the spin glass phase, the analytic continuation from positive integer to real numbers of replicas is found to be non-unique. However, replica symmetry is not broken. These conclusions remain true in a 1/p expansion about the p ~ ~ limit. J....

We report here on low field dc and ac magnetic susceptibility measurements on the compounds SrCreFeq-,GaXOlg with x = 0 to x = 4. We have determined their magnetic phase diagram and proved that increasing the Ga content in the structure we cross from fernmagnetic-like ordering and spin glass reentrance t o pure spin glass behaviour and finally to the disapearance of any magnetic ordering in SrC...

Quenched and Annealed Ising Spin Glass by Pierluigi Contucci SISSA/ISAS Via Beirut 4, 34014 Trieste , Italy and Universit a di Roma \La Sapienza", Dipartimento di Fisica G10 Teorico P.le Aldo Moro, 00185 Rome, Italy Abstract Using the cluster expansion technique, we estimate, uniformly in the volume, the difference between the quenched and annealed free energy in the high temperature phase of a...

We present results of a rigorous analysis of the k J king spin glass on the Bethe lattice with uncorrelated boundary conditions. We derive phase diagrams as functions of temperature 'us. percentage of ferromagnetic bonds, and, when half of the bonds are ferromagnetic, temperature 'us. external field. Critical exponents are also determined. Using bifurcation theory, we establish the existence of...

Study of the clusteror community structure of complex networks makes an important contribution to the understanding of networks at a functional level. Despite the many efforts, no definition of community has been agreed on and important aspects such as the statistical significance and theoretical limits of community detection are not well understood. We show how the problem of community detecti...