相关论文: Optimization of Mean-field Spin Glasses
One of the key predictions of Parisi's broken replica symmetry theory of spin glasses is the existence of a phase transition in an applied field to a state with broken replica symmetry. This transition takes place at the de Almeida-Thouless…
We study the Langevin dynamics of the standard random heteropolymer model by mapping the problem to a supersymmetric field theory using the Martin-Siggia-Rose formalism. The resulting model is solved non-perturbatively employing a Gaussian…
We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic…
Constraint Satisfaction Problems (CSPs) lie at the heart of complexity theory and find application in a plethora of prominent tasks ranging from cryptography to genetics. Classical approaches use Hopfield networks to find approximate…
We have focused in the paper on the most prominent and intensively studied S=1 pseudospin formalism for extended bosonic Hubbard model (EHBM) with truncation of the on-site Hilbert space to the three lowest occupation states n = 0, 1, 2.…
Finding the ground states of the Ising Hamiltonian [1] maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence, and social network. So far no efficient classical and quantum…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…
Out-of-equilibrium dynamics of non-integrable Hamiltonian many-body quantum systems are characterized by highly entangled wave functions. Near-maximal entanglement arises in systems exhibiting thermalization or pre-thermalization, where the…
Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the…
Spin glass systems as lattices of disordered magnets with random interactions have important implications within the theory of magnetization and applications to a wide-range of hard combinatorial optimization problems. Nevertheless, despite…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
We review some of the most recent results on the dynamics of the Hamiltonian Mean Field (HMF) model, a systems of N planar spins with ferromagnetic infinite-range interactions. We show, in particular, how some of the dynamical anomalies of…
Spin glasses featured by frustrated interactions and metastable states have important applications in chemistry, material sciences and artificial neural networks. However, the solution of the spin glass models is hindered by the…
All higher-spin s >= 1/2 Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It…
We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses.…
A quantum Parisi formula for the transverse field Sherrington-Kirkpatrick (SK) model is proven with an elementary mathematical method. First, a self-overlap corrected quantum model of the transverse field SK model is represented in terms of…
We consider the infinite-range deterministic spin models with Hamiltonian $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the quantization of a chaotic map of the torus. The mean field (TAP) equations are derived by summing the…
We consider ferromagnetic spin models on dilute random graphs and prove that, with suitable one-body infinitesimal perturbations added to the Hamiltonian, the multi-overlaps concentrate for all temperatures, both with respect to the thermal…
We investigate the properties of the glass phase of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential, which serves as a model of low temperature molecular or soft glasses. We solve the…
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…