Related papers: Remarks on the interpolation method
From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the…
In the three-dimensional Heisenberg spin glass in a random field we study the properties of the inherent structures that are obtained by an instantaneous cooling from infinite temperature. For not too large field the density of states…
We compute analytically the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean field model, i.e. we compute the exponentially small probability of finding a system with intensive…
We consider general mixed $p$-spin mean field spin glass models and provide a method to prove that the spectral gap of the Dirichlet form associated with the Gibbs measure is of order one at sufficiently high temperature. Our proof is based…
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking…
We study the random energy model with a hierarchical structure known as the generalized random energy model (GREM). In contrast to the original analysis by the microcanonical ensemble formalism, we investigate the GREM by the canonical…
In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…
The effective potential formalism is applied to glass forming liquids, choosing a coupling potential such that the "order parameter", conjugated to the coupling strength, is the mean square displacement of the particles from their position…
We consider sequences of large sparse random graphs whose degree distribution approaches a limit with finite mean. This model includes both the random regular graphs and the Erd\"os-Renyi graphs of constant average degree. We prove that the…
We propose a new method for exact analytical calculation of the ground-state energy of the Ising spin glass on strips. An outstanding advantage of this method over the numerical transfer matrix technique is that the energy is obtained for…
The equivalent circuit model for artificial magnetic materials based on various arrangements of split rings is generalized by taking into account losses in the substrate or matrix material. It is shown that a modification is needed to the…
We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the space and the reproducing kernel. If the volume of shells is…
We study the three-dimensional system of magnetic nanoparticle dipoles randomly oriented along quenched easy axes. Directions of the magnetic momenta are described by the Ising variables which allow the momenta to flip along their random…
A generalized Frenkel condition is proposed for use in spin hydrodynamics to relate the spin density and spin polarization (or spin chemical potential) tensors. It allows for independent treatment of electric- and magnetic-like components…
The free energy of multiple systems of spherical spin glasses with constrained overlaps was first studied in arXiv:math/0604082. The authors proved an upper bound of the constrained free energy using Guerra's interpolation. In this paper,…
An appropriate model for the random energy landscape in organic glasses is a spatially correlated Gaussian field, generated by randomly located and oriented dipoles and quadrupoles. Correlation properties of energetic disorder directly…
We introduce the ideal Gaussian glass-forming system as a model to describe the thermodynamics and dynamics of supercooled liquids on a local scale in terms of the properties of the potential energy landscape (PEL). The first ingredient is…
We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which…
Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…