Related papers: Diluted Mean-Field Spin-Glass Models at Criticalit…
Recently, a method has been proposed to obtain accurate predictions for low-temperature properties of lattice spin glasses that is practical even above the upper critical dimension, $d_c=6$. This method is based on the observation that…
We provide a strategy to find in few elementary calculations the critical exponents of the overlaps for dilute spin glasses, in absence of external field. Such a strategy is based on the expansion of a suitably perturbed average of the…
Within the replica approach to mean-field spin-glasses the transition from ergodic high-temperature behaviour to the glassy low-temperature phase is marked by the instability of the replica-symmetric saddle-point. For general spin-glass…
It is shown by means of a 1/m expansion about the large-m limit of the m-vector spin glass that the lower critical dimension of the de Almeida-Thouless line in spin glasses is equal to the lower critical dimension of the large-m limit of…
The nature of spin-glass states in a magnetic field remains a major open problem in statistical physics. The existence of the de Almeida-Thouless (dAT) transition for three-dimensional (3D) spin glasses in a field is still debated. We…
The static and dynamic susceptibilities for a general class of mean field random orthogonal spherical spin glass models are studied. We show how the static and dynamical properties of the linear and nonlinear susceptibilities depend on the…
We determine the phase transition of the Levy spin glass. A regularized model where the coupling constants smaller than some cutoff $\epsilon$ are neglected can be studied by the cavity method for diluted spin glasses. We show how to handle…
We present results of a Monte Carlo simulation of an Heisenberg Spin Glass model on a hipercubic cell of size 2 in {\it D} dimensions. Each spin interacts with {\it D} nearest neighbors and the lattice is expected to recover the completely…
We investigate the critical behavior of a three-dimensional short-range spin glass model in the presence of an external field $\eps$ conjugated to the Edwards-Anderson order parameter. In the mean-field approximation this model is described…
The de Almeida-Thouless (AT) line in Ising spin glasses is the phase boundary in the temperature $T$ and magnetic field $h$ plane below which replica symmetry is broken. Using perturbative renormalization group (RG) methods, we show that…
Vector spin glasses are known to show two different kinds of phase transitions in presence of an external field: the so-called de Almeida-Thouless and Gabay-Toulouse lines. While the former has been studied to some extent on several…
We analyze the spin glass transition in a field in finite dimension $D$ below the upper critical dimension directly at zero temperature using a recently introduced perturbative loop expansion around the Bethe lattice solution. The expansion…
We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size…
An important prediction of Mode-Coupling-Theory (MCT) is the relationship between the power- law decay exponents in the {\beta} regime. In the original structural glass context this relationship follows from the MCT equations that are…
Most of the analytical studies on spin glasses are performed by using mean-field theory and renormalization group analysis. Analytical studies on finite-dimensional spin glasses are very challenging. In this short note, a possible exten-…
Within the framework of the effective potential theory of the structural glass transition, we calculate for the p-spin model a static nonlinear susceptibility related to a four-point density correlation function, and show that it grows and…
We show several calculations to identify the critical point in the ground state in random spin systems including spin glasses on the basis of the duality analysis. The duality analysis is a profound method to obtain the precise location of…
The critical properties of short-range Ising spin-glass models, defined on a diamond hierarchical lattice of graph fractal dimension $d_{f}=2.58$, 3, and 4, and scaling factor 2 are studied via a method based on the Migdal-Kadanoff…
We investigate the L\'evy glass, a mean-field spin glass model with power-law distributed couplings characterized by a divergent second moment. By combining extensively many small couplings with a spare random backbone of strong bonds the…
We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and gauge symmetry for replicated random systems…