Related papers: Generic Ising Trees
Two-dimensional magnetic garnets exhibit complex and fascinating magnetic domain structures, like stripes, labyrinths, cells and mixed states of stripes and cells. These patterns do change in a reversible way when the intensity of an…
Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…
Two attractive and often used ideas, namely universality and the concept of a zero temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously…
We study the order parameter distribution P(q) in the 4d Ising spin glass with $\pm J$ couplings in a magnetic field. We also compare these results with simulations for the infinite ranged model (i.e. SK model.) Then we analyse our…
To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in…
Non-reciprocal interactions are a generic feature of non-equilibrium systems. We define a non-reciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for…
In this paper, we consider the Ising model on random $d$-regular graphs (with $d\ge3$) and Erd\"os-R\'enyi graphs $G(n,d/n)$ (with $d>1$) at the critical temperature. We prove that the \textit{magnetization}, i.e.\ the sum of the spins of a…
We consider the single-spin-flip dynamics of the random-field Ising model on a Bethe lattice at zero temperature in the presence of a uniform external field. We determine the average magnetization as the external field is varied from minus…
We revisit classical bounds of M. E. Fisher on the ferromagnetic Ising model, and show how to efficiently use them on an arbitrary given graph to rigorously upper-bound the partition function, magnetizations, and correlations. The results…
The zero-temperature Ising model is known to reach a fully ordered ground state in sufficiently dense random graphs. In sparse random graphs, the dynamics gets absorbed in disordered local minima at magnetization close to zero. Here, we…
We derive the analytical expression for the first finite size correction to the average free energy of disordered Ising models on random regular graphs. The formula can be physically interpreted as a weighted sum over all non…
We give a rigorous proof of the existence of spontaneous magnetization at finite temperature for the Ising spin model defined on the Sierpinski carpet fractal. The theorem is inspired by the classical Peierls argument for the two…
The Lenz-Ising model has served for almost a century as a basis for understanding ferromagnetism, and has become a paradigmatic model for phase transitions in statistical mechanics. While retaining the Ising energy arguments, we use…
We consider the zero-temperature random-field Ising model in the presence of an external field, on ladders and in one dimension with finite range interactions, for unbounded continuous distributions of random fields, and show that there is…
Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40^2. A combination of a genetic algorithm and Cluster-Exact Approximation is used. For…
The four dimensional Gaussian random field Ising magnet is investigated numerically at zero temperature, using samples up to size $64^4$, to test scaling theories and to investigate the nature of domain walls and the thermodynamic limit. As…
We consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the spin configuration onto the parameter, which drives the…
The Ising model was generalized to a system of cells interacting exclusively by presence of shared spins. Within the cells there are interactions of any complexity, the simplest intracell interactions come down to the Ising model. The…
We consider the full probability distribution for the transverse magnetization of a finite subsystem in the transverse field Ising chain. We derive a determinant representation of the corresponding characteristic function for general…
We study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering Monte Carlo and branch, cut, and price…