Related papers: Zero-temperature Glauber dynamics on small-world n…
We study the ferromagnetic random field Ising model (RFIM) on a graph $G=(V,E)$ having maximal degree $\Delta$, where the external field at each vertex is an i.i.d. random variable. When the random field distribution is sufficiently…
We find the exact critical temperature $T_c$ of the nearest-neighbor ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary degree distribution $P(k)$. We observe an anomalous behavior of the magnetization, magnetic…
We study analytically the one-dimensional Ising model with a random binary distribution of ferromagnetic and antiferromagnetic exchange couplings at zero temperature. We introduce correlations in the disorder by assigning a dimer of one…
The exact determination of ground states of small systems is used in a scaling study of the random-field Ising model. While three variants of the model are found to be in the same universality class in 3 dimensions, the Gaussian and bimodal…
We introduce an alternative thermal diffusive dynamics for the spin-S Ising ferromagnet realized by means of a random walker. The latter hops across the sites of the lattice and flips the relevant spins according to a probability depending…
There is proposed a model of scale-free random graphs which are locally close to the uncorrelated complex random networks with divergent $\langle k^2 \rangle$ studied in e.g. S. N. Dorogovtsev {\it et al}, Rev. Mod. Phys. {\bf 80}, 1275…
The Ising model in uncorrelated scale-free networks has been studied by means of Monte Carlo simulations. These networks are characterized by a degree (or connectivity) distribution $P(k) \sim k^{-\gamma}$. The ferromagnetic-paramagnetic…
On directed} Barabasi-Albert and Small-World networks the Ising model with spin S=1, 3/2 and 2 is now studied through Monte Carlo simulations. In this model, the order-disorder phase transition of the order parameter is well defined on…
In this paper we consider the Glauber dynamics for the one-dimensional Ising model with dissipation, in a mesoscopic regime obtained by letting inverse temperature and volume go to infinity with a suitable scaling. In this limit the…
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…
We study the second-moment correlation length and the reduced susceptibility of two ferromagnetic Ising models with zero-temperature ordering. By introducing a scaling variable motivated by high-temperature series expansions, we are able to…
Networks that have power-law connectivity, commonly referred to as the scale-free networks, are an important class of complex networks. A heterogeneous mean-field approximation has been previously proposed for the Ising model of the…
We study the ferromagnetic Ising model on the Sierpinski gasket (SG), where the spin-spin interactions depends on the direction. Using the renormalization group method, we show that the ratios of the correlation lengths restore the isotropy…
We analytically investigate the kinetic Gaussian model and the one-dimensional kinetic Ising model on two typical small-world networks (SWN), the adding-type and the rewiring-type. The general approaches and some basic equations are…
In zero-temperature Glauber dynamics, vertices of a graph are given i.i.d.~initial spins $\sigma_x(0)$ from $\{-1,+1\}$ with $\mathbb{P}_p(\sigma_x(0) = +1)=p$, and they update their spins at the arrival times of i.i.d. Poisson processes to…
We investigate the non-equilibrium two-time correlation and response functions and the associated fluctuation-dissipation ratio for the ferromagnetic Ising chain with Glauber dynamics. The scaling behavior of these quantities at low…
In this paper, we prove a general result concerning finite-range, attractive interacting particle systems on $\{-1, 1\}^{\mathbb{Z}^d}$. If the particle system has a unique stationary measure and, in a precise sense, relaxes to this…
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling…
The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reaveals that the Luttinger liquid spin susceptibility…
We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the…