Related papers: Exact solution of a 2d random Ising model
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 consider Ising model on edge-dual of uncorrelated random networks with arbitrary degree distribution. These networks have a finite clustering in the thermodynamic limit. High and low temperature expansions of Ising model on the edge-dual…
Dynamical Ising machines are based on continuous dynamical systems evolving from a generic initial state to a state strongly related to the ground state of the classical Ising model on a graph. Reaching the ground state is equivalent to…
We provide a simple characterization of the critical temperature for the Ising model on an arbitrary planar doubly periodic weighted graph. More precisely, the critical inverse temperature \beta for a graph G with coupling constants…
We consider layered two-dimensional Ising and directed walk models and show that the two problems are inherently related. The information about the zero-field thermodynamical properties of the Ising model is contained into the transfer…
Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In…
The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the…
We propose an interpretation of previous experimental and numerical experiments, showing that for a large class of systems, distributions of global quantities are similar to a distribution originally obtained for the magnetization in the…
The Kawasaki model is not exactly solvable as any choice of the exchange rate ($w_{jj'}$) which satisfies the detailed balance condition is highly nonlinear. In this work we address the issue of writing $w_{jj'}$ in a best possible linear…
We investigate the zero-temperature glassy transitions in the square-lattice +- J Ising model, with bond distribution $P(J_{xy}) = p \delta(J_{xy} - J) + (1-p) \delta(J_{xy} + J)$; p=1 and p=1/2 correspond to the pure Ising model and to the…
The classical Ising chain is the paradigm for the non-existence of phase transitions in 1D systems and was solved by Ernst Ising one hundred years ago. More recently, a decorated two leg Ising ladder has received interest for the curious…
We investigate the learning performance of the pseudolikelihood maximization method for inverse Ising problems. In the teacher-student scenario under the assumption that the teacher's couplings are sparse and the student does not know the…
The Ising model is well-known for illustrating the fundamental characteristics of phase transitions in closed systems. In this article, we propose a generalization of the two-dimensional Ising model to open systems, considering the…
We consider infinite or periodic 2D triangular Ising lattices with arbitrary positive or negative nearest-neighbor couplings $K_i(\vec{r})$, where $\vec{r}$ and $i$ indicate the bond position and orientation, respectively. Iterative…
We study the critical behavior of a general class of cubic-symmetric spin systems in which disorder preserves the reflection symmetry $s_a\to -s_a$, $s_b\to s_b$ for $b\not= a$. This includes spin models in the presence of random…
We consider the stochastic dynamics of Ising ferromagnets (either pure or random) near zero temperature. The master equation satisfying detailed balance can be mapped onto a quantum Hamiltonian which has an exact zero-energy ground state…
The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical…
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…
The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…
In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the \sus and the free energy are obtained for the quenched bond-diluted Ising model in $d = 3$--5 dimensions. They…