Related papers: Remarks on the interpolation method
We study the high-temperature regime of a mean-field spin glass model whose couplings matrix is orthogonally invariant in law. The magnetization of this model is conjectured to satisfy a system of TAP equations, originally derived by Parisi…
This paper constitutes the first part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a general Mattis interaction part. In this paper, we focus on…
A model of spinless interacting electrons in presence of randomness is examined using an extended dynamical mean-field formulation. When the interaction strength is large as compared to the Fermi energy, a low temperature glassy phase is…
We study Derrida's generalized random energy model in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters.…
We study the equilibrium properties of the Blume-Emery-Griffiths model with bilinear quenched disorder in the case of attractive as well as repulsive biquadratic interactions. The global phase diagram of the system is calculated in the…
Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs…
Many mean-field models have been introduced to describe the mechanical behavior of glassy materials. They often rely on averages performed over distributions of elements or states. We here underline that averaging is a more intricate…
connected spin-glass models with a discontinuous transition. In the thermodynamic limit the equilibrium properties in the high temperature phase are described by the schematic Mode Coupling Theory of super-cooled liquids. We show that {\it…
We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent…
We analyze exact ground-state energies of two-dimensional Ising spin glasses with either Gaussian or bimodal nearest-neighbor interactions for large system sizes and for three types of boundary conditions: free on both axes, periodic on…
We compute the pressure of the random energy model (REM) and generalized random energy model(GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra's ``broken replica symmetry bounds",and…
The interpolation method for mean field spin glass models developed by Guerra and Talagrand is extended to a quantum mean field spin glass model. This extension enables us to obtain both replica-symmetric (RS) and one step replica-symmetry…
We present results from simulations of the gauge glass model in three dimensions using the parallel tempering Monte Carlo technique. Critical fluctuations should not affect the data since we equilibrate down to low temperatures, for…
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…
We introduce some applications of Stein's method in the high temperature analysis of spin glasses. Stein's method allows the direct analysis of the Gibbs measure without having to create a cavity. Another advantage is that it gives limit…
We present sufficient conditions on a smooth uniformly flat hypersurface W in the unit ball to be an interpolation hypersurface or a sampling hypersurface for generalized Bergman spaces associated to the unit ball with its Bergman metric.…
We introduce simple models, inspired by previous models for froths and covalent glasses, with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems. These models are also a generalization of…
In a spin glass system on a random graph, some vertices have their spins changing among different configurations of a ground--state domain. Long range frustrations may exist among these unfrozen vertices in the sense that certain…
We present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems. Our approach is based on a generalization of the cavity method to a…
Several puzzling regularities concerning the low temperature excitations of glasses are quantitatively explained by quantizing domain wall motions of the random first order glass transition theory. The density of excitations agrees with…