Related papers: Ising's roots and the transfer-matrix eigenvalues
The earlier times of evolution of a magnetic system contain more information than we can imagine. Capturing correlation matrices G of different time evolutions of a simple testbed spin system, as the Ising model, we analyzed the density of…
On any locally-finite geometry, the stochastic Ising model is known to be contractive when the inverse-temperature $\beta$ is small enough, via classical results of Dobrushin and of Holley in the 1970's. By a general principle proposed by…
The site-decorated Ising model is introduced to advance the understanding and experimental realization of the recently discovered one-dimensional (1D) finite-temperature ultranarrow phase crossover in an external magnetic field, while…
We investigate the existence and the properties of fully separable (fully factorized) ground states in quantum spin systems. Exploiting techniques of quantum information and entanglement theory we extend a recently introduced method and…
A family of multispecies Ising models on generalized regular random graphs is investigated in the thermodynamic limit. The architecture is specified by class-dependent couplings and magnetic fields. We prove that the magnetizations,…
A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic and antiperiodic-antiperiodic boundary…
We obtain the exact physical characteristics of the triple-chain Ising model on a torus with all possible multispin interactions invariant with respect to rotation by the angle $2\pi / 3$. The exact value of the partition function in a…
We present a general procedure for calculating the exact partition function of an Ising model on a periodic chain in presence of magnetic field considering both open and closed boundary conditions. Using same procedure on a quasiperiodic…
In this work, we employed the Ising model to identify phase transitions in a magnetic system where the degree distribution of the network follows a power-law and the connections are assortatively mixed. In the Ising model, the spins assume…
Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show that a certain generating function of…
The general-purpose programmable photonic processors offer a scalable and reconfigurable solution for a wide range of RF and optical applications. Therefore, implementing photonic Ising machines using programmable processors leverages the…
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 study the ferromagnetic Ising model on the infinite $d$-regular tree under the free boundary condition. This model is known to be a factor of IID in the uniqueness regime, when the inverse temperature $\beta\ge 0$ satisfies $\tanh \beta…
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model…
The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data is in perfect agreement with the…
The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and…
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic…
We investigate the spin-spin correlation functions of Ising magnets at complex values of the temperature, T. For one-dimensional chain and ladder systems, we show the existence of a kind of helimagnetic order in the vicinity of contours…
We propose the mapping of polynomial of degree 2S constructed as a linear combination of powers of spin-$S$ (for simplicity, we called as spin-$S$ polynomial) onto spin-crossover state. The spin-$S$ polynomial in general can be projected…
The application of the collective variables method to the study of the behaviour of nonuniversal characteristics of the system in the critical region is illustrated by an example of the order parameter. Explicit expressions for the order…