Related papers: Metastable configurations of spin models on random…
Monadic stability and the more general monadic dependence (or NIP) are tameness conditions for classes of logical structures, studied in the 80's in Shelah's classification program in model theory. They recently emerged in algorithmic and…
The spin-1 quantum Ising systems with three-spin interactions on two-dimensional triangular lattices are studied by mean-field method. The thermal variations of order parameters and phase diagrams are investigated in detail. The stable,…
We explore the effect of single-particle level fluctuations on the Stoner instability in a QD with a strong spin-orbit coupling in the framework of the universal Hamiltonian with the Ising exchange interaction. We reduce the problem to…
In the many fields in which the Ising model is applied nowadays, the spin variables are often assumed to be of spin-class $\{-1,1\}$ or $\{0,1\}$, even though for any mix of binary real valued spin-classes a proper Ising model distribution…
We study the J1-J2 Ising model on the square lattice using the random local field approximation (RLFA) and Monte Carlo (MC) simulations for various values of the ratio p = J2/|J1| with antiferromagnetic coupling J2, ensuring spin…
In order to elucidate the relationship between rate-independent hysteresis and metastability in disordered systems driven by an external field, we study the Gaussian RFIM at T=0 on regular random graphs (Bethe lattice) of finite…
We study numerically the phase-ordering kinetics following a temperature quench of the Ising model with single spin flip dynamics on a class of graphs, including geometrical fractals and random fractals, such as the percolation cluster. For…
We study a one--dimensional Ising spin systems with ferromagnetic, long--range interaction decaying as $n^{-2+\a}$, $\a \in [0,\frac 12]$, in the presence of external random fields. We assume that the random fields are given by a collection…
The statistical mechanics of spin models, such as the Ising or Potts models, on generic random graphs can be formulated economically by considering the N --> 1 limit of Hermitian matrix models. In this paper we consider the N --> 1 limit in…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified…
Using a field-theoretical representation of the Tanaka-Edwards integral we develop a method to systematically compute the number N_s of 1-spin-stable states (local energy minima) of a glassy Ising system with nearest-neighbor interactions…
During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary (`spin') variables with observed means and covariances.…
We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling…
We develop a mean-field theory for random quantum spin systems using the spin coherent state path integral representation. After the model is reduced to the mean field one-body Hamiltonian, the integral is analyzed with the aid of several…
We elucidate that the nearly phase-ordered active XY spins in contact with a conserved, diffusing species on a substrate can be stable. For wide-ranging model parameters, it has stable uniform phases robust against noises. These are…
Asymmetric Ising model, in which coupled spins affect each other differently, plays an important role in diverse fields, from physics to biology to artificial intelligence. We show that coupled parametric oscillators provide a…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…