Related papers: Gibbs Measures for Long-Range Ising Models
We consider polynomial long-range Ising models in one dimension, with ferromagnetic pair interactions decaying with power $2-\alpha$ (for $0 \leq \alpha < 1$), and prepared with randomly chosen boundary conditions. We show that at low…
We consider one-dimensional long-range spin models (usually called Dyson models), consisting of Ising ferromagnets with slowly decaying long-range pair potentials of the form $\frac{1}{|i-j|^{\alpha}}$ mainly focusing on the range of slow…
We study the one dimensional Ising model with ferromagnetic, long range interaction which decays as |i-j|^{-2+a}, 1/2< a<1, in the presence of an external random filed. we assume that the random field is given by a collection of independent…
We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not $g$-measures. The main ingredient in the proof is the occurrence of an…
We study single-site stochastic and deterministic transforma- tions of one-dimensional Gibbs measures in the uniqueness regime with infinite-range interactions. We prove conservation of Gibbsianness and give quantitative estimates on the…
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…
We consider the long-range random field Ising model in dimension $d = 1, 2$, whereas the long-range interaction is of the form $J_{xy} = |x-y|^{-\alpha}$ with $1< \alpha < 3/2$ for $d=1$ and with $2 < \alpha \leq 3$ for $d = 2$. Our main…
Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin…
In this paper, we detail and complete the existing characterizations of the decimation of the Ising model on $\Z^2$ in the generalized Gibbs context. We first recall a few features of the Dobrushin program of restoration of Gibbsianness and…
Dimensional correspondences have a long history in critical phenomena. Here, we review the effective dimension approach, which relates the scaling exponents of a critical system in $d$ spatial dimensions with power-law decaying interactions…
We extend proofs of non-Gibbsianness of decimated Gibbs measures at low temperatures to include long-range, as well as vector-spin interactions. Our main tools consist in a two-dimensional use of ``Equivalence of boundary conditions'' in…
Ising model is a widely studied class of models in quantum computation. In this paper we investigate the computational characteristics of the random field Ising model (RFIM) with long-range interactions that decays as an inverse polynomial…
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any…
We study the effect of a one-dimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber dynamics in all sites and additional…
We investigate the critical behavior of the one-dimensional Ising model with long-range interactions using the functional renormalization group in the local potential approximation (LPA), and compare our findings with Dyson's hierarchical…
The critical behavior of Ising model on a one-dimensional network, which has long-range connections at distances $l>1$ with the probability $\Theta(l)\sim l^{-m}$, is studied by using Monte Carlo simulations. Through studying the Ising…
We study the ferromagnetic Ising model with long-range interactions in two dimensions. We first present results of a Monte Carlo study which shows that the long-range interactions dominate over the short-range ones in the intermediate…
We consider the random transverse-field Ising model in $d=3$ dimensions with long-range ferromagnetic interactions which decay as a power $\alpha > d$ with the distance. Using a variant of the strong disorder renormalization group method we…
A spin-glass transition occurs both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance.…
We consider a measure given as the continuum limit of a one-dimensional Ising model with long-range translationally invariant interactions. Mathematically, the measure can be described by a self-interacting Poisson driven jump process. We…