Related papers: Approximate dynamical eigenmodes of the Ising mode…
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…
Using Monte Carlo simulations we study the Ising model with spin S=1/2 and 1 on {\it directed} and {\it undirected} Erd\"os-R\'enyi (ER) random graphs, with $z$ neighbors for each spin. In the case with spin S=1/2, the {\it undirected} and…
We study dynamical spin correlations in a dissipative XXZ spin chain subject to uniform local spin-loss and pumping. Starting from a mixed steady state that is featureless albeit possessing finite magnetization, rich dynamics emerges in…
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…
We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states having product structure in fermionic momentum-space and…
The fractal structure and scaling properties of a 2d slice of the 3d Ising model is studied using Monte Carlo techniques. The percolation transition of geometric spin (GS) clusters is found to occur at the Curie point, reflecting the…
The selfconsistent approach to the 2D Ising Model with quenched random bonds is extended to the full lattice theory of four real fermions. The additional degrees of freedom, neglected in the renormalization-group theory, lead to a new phase…
We study the domain growth of the one-dimensional kinetic Ising model under the competing influence of Glauber dynamics at temperature T and Kawasaki dynamics with a configuration-independent rate. The scaling of the structure factor is…
We consider the Ising model at its critical temperature with external magnetic field $ha^{15/8}$ on $a\mathbb{Z}^2$. We give a purely probabilistic proof, using FK methods rather than reflection positivity, that for $a=1$, the correlation…
We solve the Langevin dynamics of d-dimensional ferromagnetic spherical models with interactions that decay with distance as r^-(d+sigma). The long time dynamics of correlations and responses are studied in the different dynamical regimes…
We study classical Ising spin-$\frac{1}{2}$ models on the 2D square lattice with ferromagnetic or antiferromagnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The complex Boltzmann weights of spin…
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 use simple models (the Ising model in one and two dimensions, and the spherical model in arbitrary dimension) to put to the test some recent ideas on the slow dynamics of nonequilibrium systems. In this review the focus is on the…
We comprehensively study non-equilibrium relaxation and aging processes in the two-dimensional random-site Ising model through numerical simulations. We discuss the dynamical correlation length as well as scaling functions of various…
We have recently shown that in non-equilibrium spin systems at criticality the limit $\Xin$ of the fluctuation-dissipation ratio X(t,tw) for t >> tw >> 1 can be measured using observables such as magnetization or energy [Phys. Rev.\ E {\bf…
The dynamics of an asymmetric kinetic Ising model is studied. Two schemes for improving the existing mean-field description are proposed. In the first scheme, we derive the formulas for instantaneous magnetization, equal-time correlation,…
We consider the Ising model on the square lattice with biaxially correlated random ferromagnetic couplings, the critical point of which is fixed by self-duality. The disorder represents a relevant perturbation according to the extended…
We study the early time dynamics of the 2d ferromagnetic Ising model instantaneously quenched from the disordered to the ordered, low temperature, phase. We evolve the system with kinetic Monte Carlo rules that do not conserve the order…
The dynamical response of an Ising ferromagnet to a plane polarised standing magnetic field wave is modelled and studied here by Monte Carlo simulation in two dimensions. The amplitude of standing magnetic wave is modulated along the…
We study a lattice model of a single magnetic polymer chain, where Ising spins are located on the sites of a lattice self-avoiding walk in $d=2$. We consider the regime where both conformations and magnetic degrees of freedom are dynamic,…