Related papers: Near optimal configurations in mean field disorder…
In realistic disordered systems, such as the Edwards-Anderson (EA) spin glass, no order parameter, such as the Parisi overlap distribution, can be both translation-invariant and non-self-averaging. The standard mean-field picture of the EA…
We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the…
We study numerically the configuration space at low energy of electron glasses. We consider systems with Coulomb interactions, short-range interactions and no interactions. First, we calculate the integrated density of configurations as a…
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 employ a novel algorithm using a quasi-exact embedded-cluster matching technique as minimization method within a genetic algorithm to reliably obtain numerically exact ground states of the Edwards-Anderson XY spin glass model with…
According to the mean-field glass theory, the (free) energy landscape of disordered systems is hierarchical and ultrametric if they belong to the full-replica-symmetry-breaking universality class. However, examining this theoretical picture…
In this work, we consider general exchangeable quantum mean-field Hamiltonian such as the prominent quantum Curie-Weiss model under the influence of a random external field. Despite being arguably the simplest class of disordered quantum…
We analyze the low-temperature behavior of mean-field equations of Thouless, Anderson, and Palmer (TAP). We demonstrate that degeneracy in free energy makes the low-temperature TAP states unstable. Different solutions of the TAP equations,…
We study the spin glass system consisting of a Random Energy Model coupled with a random magnetic field. This system was investigated by de Oliveira Filho, da Costa and Yokoi (Phys. Rev. E 74 [2006]) who computed the free energy. In this…
We study first order quantum phase transitions in mean-field spin glasses. We solve the quantum Random Energy Model using elementary methods and show that at the transition the eigenstate suddenly projects onto the unperturbed ground state…
We construct and analyze a family of $M$-component vectorial spin systems which exhibit glass transitions and jamming within supercooled paramagnetic states without quenched disorder. Our system is defined on lattices with connectivity…
We study the energy of a ferromagnetic/antiferromagnetic frustrated spin system with values on two disjoint circumferences of the 3-dimensional unit sphere in a one-dimensional and two-dimensional domain. It consists on the sum of a term…
We introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra…
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…
An energy functional for orbital based $O(N)$ calculations is proposed, which depends on a number of non orthogonal, localized orbitals larger than the number of occupied states in the system, and on a parameter, the electronic chemical…
The quantum random energy model provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body localization - delocalization (MBLD) transition when viewed as a closed quantum system.…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…
We study rough high-dimensional landscapes in which an increasingly stronger preference for a given configuration emerges. Such energy landscapes arise in glass physics and inference. In particular we focus on random Gaussian functions, and…
Combinatorial optimization algorithms which compute exact ground state configurations in disordered magnets are seen to exhibit critical slowing down at zero temperature phase transitions. Using arguments based on the physical picture of…
This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and…