Related papers: Interpreting the Ising Model: The Input Matters
We introduce and analyze an exactly soluble one-dimensional Ising model with long range interactions which exhibits a mixed order transition (MOT), namely a phase transition in which the order parameter is discontinuous as in first order…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
Results are presented for the kinetics of domain growth of a two-dimensional Ising spin model with competing interactions quenched from a disordered to a striped phase. The domain growth exponent are $\beta=1/2$ and $\beta=1/3$ for…
Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…
We study the ordering kinetics of a generalization of the voter model with long-range interactions, the $p$-voter model, in one dimension. It is defined in terms of boolean variables $S_{i}$, agents or spins, located on sites $i$ of a…
We study the Ising model on a two-community stochastic block model, where $n$ spins are split into two equal groups with inter-community interaction parameter $\alpha_n\in[0,1]$. We provide a complete characterization of the phase diagram…
Interdependence is a fundamental ingredient to analyze the stability of many real-world complex systems featuring functional liasons. Yet, physical realizations of this coupling are still unknown, due to the lack of a theoretical framework…
Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…
We give a short non-technical introduction to the Ising model, and review some successes as well as challenges which have emerged from its study in probability and mathematical physics. This includes the infinite-volume theory of phase…
The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the…
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a…
In recent years, Ising prior with the network information for the "in" or "out" binary random variable in Bayesian variable selections has received more and more attentions. In this paper, we discover that even without the informative prior…
We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical expressions…
We study the dynamics of entanglement in the one-dimensional spin-1/2 XY model in the presence of a transverse magnetic field. A pair of spins are considered as an open quantum system, while the rest of the chain plays the role of the…
The Ising model is an equilibrium stochastic process used as a model in several branches of science including magnetic materials, geophysics, neuroscience, sociology and finance. Real systems of interest have finite size and a fixed…
We consider several aspects of non-periodic Ising models in one and two dimensions. Here we are not interested in random systems, but rather in models with intrinsic long-range aperiodic order. The most prominent examples in one dimension…
The d-dimensional n-spin facilitated kinetic Ising model is studied analytically starting from usual master equations and their transformation into a Fock-space representation. The evolution of relevant operators is rewritten in terms of a…
The $d$-dimensional long-range Ising model, defined by spin-spin interactions decaying with the distance as the power $1/r^{d+s}$, admits a second order phase transition with continuously varying critical exponents. At $s = s_*$, the phase…
An improved unified formulation based on the effective field theory is introduced for a spin-1 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the…
Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that…