Related papers: Gaussian Mean Fields Lattice Gas
We study numerically the Sherrington--Kirkpatrick model as function of the magnetic field h, with fixed temperature T=0.6 Tc. We investigate the finite size scaling behavior of several quantities, such as the spin glass susceptibility,…
We present a method to numerically obtain low-energy effective models based on a unitary transformation of the ground state. The algorithm finds a unitary circuit that transforms the ground state of the original model to a projected…
We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…
We discuss the energy distribution of free-electron Fermi-gas, a problem with a textbook solution of Gaussian energy fluctuations in the limit of a large system. We find that for a small system, characterized solely by its heat capacity…
We discuss a general formalism that allows study of transitions over barriers in spin glasses with long-range interactions that contain large but finite number, $N$, of spins. We apply this formalism to the Sherrington-Kirkpatrick model…
We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of…
We consider a classical lattice gas that consists of more than one "species" of particles (like a spin-3/2 Ising model or the atomic limit of the extended Hubbard model), whose ground-state phase diagram is macroscopically degenerate. This…
Marginal stability is the notion that stability is achieved, but only barely so. This property constrains the ensemble of configurations explored at low temperature in a variety of systems, including spin, electron and structural glasses. A…
We introduce Gutzwiller conjugate gradient minimization (GCGM) theory, an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. GCGM uses the Gutzwiller wave function but does not use the commonly…
Due to an extremely rugged structure of the free energy landscape, the determination of spin-glass ground states is among the hardest known optimization problems, found to be NP-hard in the most general case. Owing to the specific structure…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
Computing Gaussian ground states via variational optimization is challenging because the covariance matrices must satisfy the uncertainty principle, rendering constrained or Riemannian optimization costly, delicate, and thus difficult to…
We focus on spherical spin glasses whose Parisi distribution has support of the form $[0,q]$. For such models we construct paths from the origin to the sphere which consistently remain close to the ground-state energy on the sphere of…
The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is…
In a region above the Almeida-Thouless line, where we are able to control the thermodynamic limit of the Sherrington-Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are…
We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-like atoms in optical lattices that can be effectively described by the two-band spin-$1/2$ Hubbard model including the Hund's exchange coupling…
The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quantum gravity near the Planck scale is implemented on deriving the thermodynamics of ideal Quark-Gluon Plasma (QGP) consisting of two massless…
A semiclassical analysis based on spin-coherent states is used to establish a classification and formulae for the spectral gap of mean-field spin Hamiltonians. For gapped systems we provide a full description of the low-energy spectra based…
A dilute gas of particles with short range interactions is considered in a shearing stationary state. A Gaussian thermostat keeps the total kinetic energy constant. For infinitely many particles it is shown that the thermostat becomes a…
By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…