Related papers: Optimization of the Sherrington-Kirkpatrick Hamilt…
The behavior of the nonlinear susceptibility $\chi_3$ and its relation to the spin-glass transition temperature $T_f$, in the presence of random fields, are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied…
We discuss the Sherrington-Kirkpatrick mean-field version of a spin glass within the distributional zeta-function method (DZFM). In the DZFM, since the dominant contribution to the average free energy is written as a series of moments of…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…
Hysteretic optimization is a heuristic optimization method based on the observation that magnetic samples are driven into a low energy state when demagnetized by an oscillating magnetic field of decreasing amplitude. We show that hysteretic…
We investigate thermodynamics of a single classical particle placed in a spherical box of a finite radius $R$ and subject to a superposition of a $N-$dimensional Gaussian random potential and the parabolic potential with the curvature…
The distribution of solutions of the Thouless-Anderson-Palmer equation is studied by extensive numerical experiments for fully connected 3-body interaction Ising spin glass models in a level of annealed calculation. A recent study predicted…
We consider a spherical spin system with pure 2-spin spherical Sherrington-Kirkpatrick Hamiltonian with ferromagnetic Curie-Weiss interaction. The system shows a two-dimensional phase transition with respect to the temperature and the…
We consider optimization problems for complex systems in which the cost function has a multivalleyed landscape. We introduce a new class of dynamical algorithms which, using a suitable annealing procedure coupled with a balanced…
While obtaining optimal algorithms for the most important problems in the LOCAL model has been one of the central goals in the area of distributed algorithms since its infancy, tight complexity bounds are elusive for many problems even when…
The Wigner spiked model in a mismatched setting is studied with the finite temperature Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick model with added Mattis interaction. The exact solution of the…
Using a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The…
In this paper a multi-scale version of the Sherrington and Kirkpatrick model is introduced and studied. The pressure per particle in the thermodynamical limit is proved to obey a variational principle of Parisi type. The result is achieved…
The free energy of the Random Energy Model at the transition point between ferromagnetic and spin glass phases is calculated. At this point, equivalent to the decoding error threshold in optimal codes, free energy has finite size…
Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…
Fine resolution of the discrete eigenvalues at the spectral edge of an $N\times N$ random matrix is required in many applications. Starting from a finite-size scaling ansatz for the Stieltjes transform of the maximum likelihood spectrum, we…
We consider the problem of estimating the maximal energy of quantum $p$-local spin glass random Hamiltonians, the quantum analogues of widely studied classical spin glass models. Denoting by $E^*(p)$ the (appropriately normalized) maximal…
Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three-dimensional Edwards-Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick…
We present a theory to describe the dynamics of the Sherrington- Kirkpatrick spin-glass with (sequential) Glauber dynamics in terms of deterministic flow equations for macroscopic parameters. Two transparent assumptions allow us to close…
We present an algorithm for finding ground states of two dimensional spin glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero temperature and defines an approximate…
We consider the Sherrington--Kirkpatrick spin glass model with zero external field and at inverse temperature $\beta>0$. Let $F_N(\beta)$ be the corresponding log-partition function. Under the assumption that $c_N:=N^{1/3}(1-\beta_N^2)$ is…