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The Ising model is an equilibrium stochastic process used as a model in several branches of science including magnetic materials, geophysics, neuroscience, sociology and finance. Real systems of interest have finite size and a fixed…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
The exact solution of a two-dimensional (2D) Ising model with the next nearest interactions at zero magnetic field is derived. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic representation,…
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e.,…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a…
We study the time evolution of the two-dimensional kinetic Ising model in finite systems with a non-conserved order parameter, considering nearest-neighbour interactions on the square lattice with periodic and open boundary conditions.…
The laws of quantum-critical scaling theory of quantum fidelity, dependent on the underlying system dimensionality $D$, have so far been verified in exactly solvable $1D$ models, belonging to or equivalent to interacting, quadratic…
Entanglement microscopy reveals the true quantum correlations among the microscopic building blocks of many-body systems [Nat. Commun. 16, 96 (2025)]. Using this approach, we study the multipartite entanglement of the quantum Ising model in…
We study dimensional crossover in Ising systems at complex temperatures by comparing three types of system: the infinite isotropic 2D Ising model; the infinite anisotropic 2D Ising model; and Ising ladders with a finite number of legs. In…
Permanents, hafnians, and loop-hafnians are combinatorial matrix functions closely related to perfect matchings in graphs. These matrix functions arise in the quantum amplitudes of boson configurations in bosonic networks, and the classical…
We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example…
We propose a detailed analysis of datasets generated from simulations of two-dimensional quantum spin systems using the quantum Ising model at absolute zero temperature. Our focus is on examining how fundamental physical properties, energy,…
We find an exact mapping from the generalized Ising models with many-spin interactions to equivalent Boltzmann machines, i.e., the models with only two-spin interactions between physical and auxiliary binary variables accompanied by local…
Using an efficient one and two qubit gate simulator, operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two dimensional lattice, which is periodically driven by a…
We present a set of exactly solvable Ising models, with half-odd-integer spin-S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed…
The exact solution of ferromagnetic two-dimensional (2D) Ising model with a transverse field, which can be used to describe the critical phenomena in low-dimensional quantum spin systems, is derived by equivalence between the ferromagnetic…
In 1944 Onsager published the formula for the partition function of the Ising model for the infinite square lattice. He was able to express the internal energy in terms of a special function, but he left the free energy as a definite…
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…
The scaling function of the 2D Ising model in a magnetic field on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer matrix approach. The use of the Aharony-Fisher non-linear scaling…