Related papers: On Marginal Stability in Low Temperature Spherical…
In this review we define and discuss metastates, mathematical tools with general applicability to thermodynamic systems which are particularly useful when working with disordered or inhomogeneous short-range systems. In an infinite such…
An inequality of the eigenvalues of the reduced density matrix $\rho_2$ at finite temperature in the Hubbard model is obtained by means of the Bogolyubov inequality. The quasi-average of $\tilde{S}^{+}$ in a simple symmetry-breaking…
Complex free-energy landscapes with many local minima separated by large barriers are believed to underlie glassy behavior across diverse physical systems. This is the heuristic picture associated with replica symmetry breaking (RSB) in…
Different sets of metastable states can be reached in glassy systems below some transition temperature depending on initial conditions and details of the dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model with…
We present a technique to generate relations connecting pure state weights, overlaps, and correlation functions in short-range spin glasses. These are obtained directly from the unperturbed Hamiltonian and hold for general coupling…
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…
Glassiness occurs when disorder and frustration cause local degrees of freedom to freeze despite the lack of long-range order. In systems of interacting bosons, such glassiness may involve a purely quantum degree of…
We identify a special class of multi-species spin glass models: ones in which the species proportions serve to ''balance'' out the interaction strengths. For this class, we prove a free energy lower bound that does not require any convexity…
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry…
The core idea of stochastic stability is that thermodynamic observables must be robust under small (random) perturbations of the quenched Gibbs measure. Combining this idea with the cavity field technique, which aims to measure the free…
We quantify the parameter stability of a spherical Gaussian Mixture Model (sGMM) under small perturbations in distribution space. Namely, we derive the first explicit bound to show that for a mixture of spherical Gaussian $P$ (sGMM) in a…
We study the annealed complexity of the m-vector spin glasses in the Sherrington-Kirkpatrick limit. The eigenvalue spectrum of the Hessian matrix of the Thouless-Anderson-Palmer (TAP) free energy is found to consist of a continuous band of…
We evaluate the high temperature limit of the free energy of spin glasses on the hypercube with Hamiltonian $H_N(\sigma) = \sigma^T J \sigma$, where the coupling matrix $J$ is drawn from certain symmetric orthogonally invariant ensembles.…
The study of the low temperature phase of spin glass models by means of Monte Carlo simulations is a challenging task, because of the very slow dynamics and the severe finite size effects they show. By exploiting at the best the…
We study numerically the Hessian of low-lying minima of vector spin glass models defined on random regular graphs. We consider the two-component (XY) and three-component (Heisenberg) spin glasses at zero temperature, subjected to the action…
The search for problems where quantum adiabatic optimization might excel over classical optimization techniques has sparked a recent interest in inducing a finite-temperature spin-glass transition in quasi-planar topologies. We have…
We investigate the p-state mean-field model of the Potts glass ($2\le p \le 4$) below the continuous phase transition to a glassy phase. We find that apart from a solution with a first hierarchical level of replica-symmetry breaking (1RSB),…
The work of this thesis concerns the problem of linear low energy excitations of vector spin glass models. An analytical and numerical study is carried out, considering a fully connected random-field Heisenberg model at zero temperature, a…
We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We…
The problem of the survival of a spin glass phase in the presence of a field has been a challenging one for a long time. To date, all attempts using equilibrium Monte Carlo methods have been unconclusive. In their comment to our paper,…