Related papers: Ferromagnetic Ising Measures on Large Locally Tree…
We study the Ising model on affine preferential attachment models with general parameters. We identify the thermodynamic limit of several quantities, arising in the large graph limit, such as pressure per particle, magnetisation, and…
The main goal of the paper is to prove central limit theorems for the magnetization rescaled by $\sqrt{N}$ for the Ising model on random graphs with $N$ vertices. Both random quenched and averaged quenched measures are considered. We work…
The role of the geometric fluctuations on the multifractal properties of the local magnetization of aperiodic ferromagnetic Ising models on hierachical lattices is investigated. The geometric fluctuations are introduced by generalized…
We prove that the marginal densities of a global probability mass function in a primal normal factor graph and the corresponding marginal densities in the dual normal factor graph are related via local mappings. The mapping depends on the…
We consider a two-dimensional Ising field theory on a space with boundary in the presence of a piecewise constant boundary magnetic field which is allowed to change value discontinuously along the boundary. We assume zero magnetic field in…
We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world…
We consider an Ising model on a square grid with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution…
In this paper we investigate the computational complexity of learning the graph structure underlying a discrete undirected graphical model from i.i.d. samples. We first observe that the notoriously difficult problem of learning parities…
A model for single-domain uniaxial ferromagnetic particles with high anisotropy, the Ising model, is studied. Recent experimental observations have been made of the probability that the magnetization has not switched. Here an approach is…
Consider the Erd\H{o}s-Renyi random graph on n vertices where each edge is present independently with probability c/n, with c>0 fixed. For large n, a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring…
We present a comprehensive study for the statistical properties of random variables that describe the domain structure of a finite Ising chain with nearest-neighbor exchange interactions and free boundary conditions. By use of extensive…
We study localization properties of disordered bosons and spins in random fields at zero temperature. We focus on two representatives of different symmetry classes, hard-core bosons (XY magnets) and Ising magnets in random transverse…
We present local mappings that relate the marginal probabilities of a global probability mass function represented by its primal normal factor graph to the corresponding marginal probabilities in its dual normal factor graph. The mapping is…
The metric dimension of a graph $G$ is the minimal size of a subset $R$ of vertices of $G$ that, upon reporting their graph distance from a distingished (source) vertex $v^\star$, enable unique identification of the source vertex $v^\star$…
We prove rigorously that the ferromagnetic Ising model on any nonamenable Cayley graph undergoes a continuous (second-order) phase transition in the sense that there is a unique Gibbs measure at the critical temperature. The proof of this…
The purpose of this modest note is to point out that the proof of the recent result of Huchcroft concerning continuity of phase transition in Bernoulli percolation is applicable to the setting of the Ising model with free boundary…
We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar statement is proven for the $\lambda \phi^4$…
We study the generation and propagation of local perturbations in a quantum many-body spin system. In particular, we study the Ising model in transverse field in the presence of a local field defect at one edge. This system possesses a rich…
We consider the stochastic dynamics near zero-temperature of the random ferromagnetic Ising model on a Cayley tree of branching ratio $K$. We apply the Boundary Real Space Renormalization procedure introduced in our previous work (C.…
The Ising model with ferromagnetic couplings on the Hanoi networks is analyzed with an exact renormalization group. In particular, the fixed-points are determined and the renormalization-group flow for certain initial conditions is…