Related papers: Geometry of spherical spin glasses

In the present paper we analyze the critical properties of a quantum spherical spin glass model with short range, random interactions. Since the model allows for rigorous detailed calculations, we can show how the effective partition…

Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design…

We introduce and analytically study a generalized p-spin glass like model that captures some of the main features of attractive glasses, recently found by Mode Coupling investigations, such as a glass/glass transition line and dynamical…

The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost…

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…

The number $\langle N_s\rangle$ of solutions of the equations of Thouless, Anderson and Palmer for p--spin interaction spin glass models is calculated. Below a critical temperature $T_c$ this number becomes exponentially large, as it is in…

Closed formulas in terms of double sums of Clebsch-Gordan coefficients are computed for the evaluation of bra-ket spherical harmonic overlap integrals of a wide class of trigonometric functions. These analytical expressions can find useful…

Topological constraint theory has become an increasingly popular tool to predict the compositional dependence of glass properties or pinpoint promising compositions with tailored functionalities. This approach reduces complex disordered…

In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function $\sigma:[0,1]^4\to\{-1,+1\}$, and one can…

We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…

We derive Thouless-Anderson-Palmer (TAP) equations for quantum disordered systems. We apply them to the study of the paramagnetic and glassy phases in the quantum version of the spherical p spin-glass model. We generalize several useful…

We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense,…

Critical dynamics in various glass models including those described by mode coupling theory is described by scale-invariant dynamical equations with a single non-universal quantity, i.e. the so-called parameter exponent that determines all…

The mean field spin glass model is analyzed by a combination of mathematically rigororous methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural…

The gauge theory of spin glasses and statistical-mechanical formulation of error-correcting codes are reviewed with an emphasis on their similarities. For the gauge theory, we explain the functional identities on dynamical autocorrelation…

Hierarchical spin-glasses are Ising spin models defined by recursively coupling together two equally-sized sub-systems. In this work a new hierarchical spin system is introduced wherein the sub-systems are recursively coupled together…

We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent…

We study a two-dimensional compressible Ising spin glass at constant volume. The spin interactions are coupled to the distance between neighboring particles in the Edwards-Anderson model with +/- J interactions. We find that the energy of a…

We introduce a new approach to studying spherical spin glass dynamics based on differential inequalities for one-time observables. Using this approach, we obtain an approximate phase diagram for the evolution of the energy $H$ and its…

Recent high precision experimental results on spin-glass films ask for a detailed understanding of the domain-growth dynamics of two-dimensional spin glasses. To achieve this goal, we numerically simulate the out-equilibrium dynamics of the…