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Using a lattice-gas description of the low-energy degrees of freedom of the quantum Heisenberg antiferromagnet on the frustrated two-leg ladder and bilayer lattices we examine the magnetization process at low temperatures for these spin…
This paper presents a systematic study of the application of convolutional neural networks (CNNs) as an efficient and versatile tool for the analysis of critical and low-temperature phase states in spin system models. The problem of…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…
Hard combinatorial optimization problems, often mapped to Ising models, promise potential solutions with quantum advantage but are constrained by limited qubit counts in near-term devices. We present an innovative quantum-inspired framework…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
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…
Dynamical Ising machines are actively investigated from the perspective of finding efficient heuristics for NP-hard optimization problems. However, the existing data demonstrate super-polynomial scaling of the running time with the system…
A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order…
We report a nuclear magnetic resonance experiment, which simulates the quantum transverse Ising spin system in a triangular configuration and further show that the monogamy of quantum correlations can be used to distinguish between the…
In this paper we consider a 2d random Ising system on a square lattice with nearest neighbour interactions. The disorder is short range correlated and asymmetry between the vertical and the horizontal direction is admitted. More precisely,…
Spin-spin correlations are calculated in frustrated hierarchical Ising models that exhibit chaotic renormalization-group behavior. The spin-spin correlations, as a function of distance, behave chaotically. The far correlations, but not the…
At low temperatures, weakly coupled spin chains develop a magnetic order that reflects the character of gapless spin fluctuations along the chains. Using nuclear magnetic resonance, we identify and characterize two ordered states in the…
The one-dimensional Ising model with its connections to several physical concepts plays a vital role in comprehension of several principles, phenomena and numerical methods. The Hamiltonian of a coupled one-dimensional dissipative spin…
Optimization problems pose challenges across various fields. In recent years, quantum annealers have emerged as a promising platform for tackling such challenges. To provide a new perspective, we develop a heuristic tensor network (TN)…
Autoregressive Neural Networks based on dense or convolutional layers have recently been shown to be a viable strategy for generating classical spin systems. Unlike these methods, sampling with transformers is commonly considered to be…
We demonstrate quantum circuit simulations of the transverse field Ising model with longitudinal fields, displaying salient features of glassy dynamics. The energy landscape and spin configurations of toy models are considered, using the…
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a new reliability property, Ising…
We propose a novel type of minor-embedding (ME) in simulated-annealing-based Ising machines. The Ising machines can solve combinatorial optimization problems. Many combinatorial optimization problems are mapped to find the ground…
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…
Here an artificial spin ice (ASI) lattice is introduced that exhibits unique Ising and non-Ising behavior under specific field switching protocols because of the inclusion of coupled nanomagnets into the unit cell. In the Ising regime, a…