Related papers: Ising model with spins S=1/2 and 1 on directed and…
We present a sufficient condition for the presence of spontaneous magnetization for the Ising model on a general graph, related to its long-range topology. Applying this condition we are able to prove the existence of a phase transition at…
We study a one parameter family of random graph models that spans a continuum between traditional random graphs of the Erd\H{o}s-R\'enyi type, where there is no underlying structure, and percolation models, where the possible edges are…
We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest neighbor (NNN) and 3-site interactions using extensive numerical simulations and a conformal field theory analysis. We show that the…
Nonequilibrium phase transition properties of a mixed Ising ferrimagnetic model consisting of spin-1/2 and spin-3/2 on a square lattice under the existence of a time dependent oscillating magnetic field have been investigated by making use…
Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing…
We analyze Ising/Curie-Weiss models on the (directed) Erd\H{o}s-R\'enyi random graph on $N$ vertices in which every edge is present with probability $p$. These models were introduced by Bovier and Gayrard [J. Stat. Phys., 1993]. We prove a…
We discuss the finite-size scaling of the ferromagnetic Ising model on random regular graphs. These graphs are locally tree-like, and in the limit of large graphs, the Bethe approximation gives the exact free energy per site. In the…
We generalize a class of Heisenberg antiferromagnets in one, two and three dimensions, which have been shown to exhibit magnetization plateaus for spin-1/2. In a certain parameter range of the general model, which is formally defined in D…
Scale-free networks are a recently developed approach to model the interactions found in complex natural and man-made systems. Such networks exhibit a power-law distribution of node link (degree) frequencies n(k) in which a small number of…
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 study the random field $p$-spin model with Ising spins on a fully connected graph using the theory of large deviations in this paper. This is a good model to study the effect of quenched random field on systems which have a sharp first…
The magnetization process of the spin-1/2 antiferromagnetic XXZ model with Ising-like anisotropy in the ground state is investigated. We show numerically that the Ising-like XXZ models on square and cubic lattices show a first-order phase…
We study the Heisenberg $S=1/2$ chain with random ferro- and antiferromagnetic couplings using quantum Monte Carlo simulations at ultra-low temperatures, converging to the ground state. Finite-size scaling of correlation functions and…
Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…
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…
Motivated by modelling in physics and other disciplines, such as sociology and psychology, we derive the mean field of the general-spin Ising model from the variational principle of the Gibbs free energy. The general-spin Ising model has…
We investigate the ferromagnetic Ising model on the Erd\H{o}s-R\'enyi random graph $\mathbb{G}(n,m)$ with bounded average degree $d=2m/n$. Specifically, we determine the limiting distribution of $\log Z_{\mathbb{G}(n,m)}(\beta,B)$, where…
On directed Barabasi-Albert networks with two and seven neighbours selected by each added site, the Ising model with spin S=1/2 was seen not to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation…
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…
On locally tree-like random graphs, we relate the random cluster model with external magnetic fields and $q\geq 2$ to Ising models with vertex-dependent external fields. The fact that one can formulate general random cluster models in terms…