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Ising model

About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.


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TL;DR: In this article, high-temperature series expansions of the partition functions for the Ising and Heisenberg models are analyzed for various values of the spin $s$ for fcc lattice for which successive coefficients are sufficiently regular for estimates of critical behavior to be made with confidence.
Abstract: High-temperature series expansions of the partition functions for the Ising and Heisenberg models are analyzed for various values of the spin $s$. The fcc lattice is used for which successive coefficients are sufficiently regular for estimates of critical behavior to be made with confidence. It is suggested that the magnetic susceptibility above the Curie temperature is of the form $A{(1\ensuremath{-}\frac{{T}_{c}}{T})}^{\ensuremath{-}\frac{4}{3}}$ for the Heisenberg model for all $s$, instead of ${A}^{\ensuremath{'}}{(1\ensuremath{-}\frac{{T}_{c}}{T})}^{\ensuremath{-}\frac{5}{4}}$ for the Ising model. Critical estimates of energy and entropy show that the magnitude of the "tail" of the specific heat anomaly is insensitive to the value of $s$, and is about 2.5 times larger for the Heisenberg than for the Ising model. The sharpness of the anomaly at the Curie point increases as $s$ increases, and on passing from the Heisenberg to the Ising model. A brief reference is made to experimental results.

132 citations

Journal ArticleDOI
TL;DR: The conformal bootstrap program for three dimensional conformal field theories with N=2 supersymmetry is implemented and universal constraints on the spectrum of operator dimensions in these theories are found.
Abstract: We implement the conformal bootstrap program for three dimensional conformal field theories with N=2 supersymmetry and find universal constraints on the spectrum of operator dimensions in these theories. By studying the bounds on the dimension of the first scalar appearing in the operator product expansion of a chiral and an antichiral primary, we find a kink at the expected location of the critical three dimensional N=2 Wess-Zumino model, which can be thought of as a supersymmetric analog of the critical Ising model. Focusing on this kink, we determine, to high accuracy, the low-lying spectrum of operator dimensions of the theory, as well as the stress-tensor two-point function. We find that the latter is in an excellent agreement with an exact computation.

132 citations

Journal ArticleDOI
TL;DR: In this paper, the authors employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of raw spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures.
Abstract: We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and physical observables for the Hubbard model. However, we are able to define an indicator based on the output of the t-SNE algorithm that shows a near perfect agreement with the antiferromagnetic structure factor of the model in two and three spatial dimensions in the weak-coupling regime. t-SNE also predicts a transition to the canted antiferromagnetic phase for the three-dimensional model when a strong magnetic field is present. We show that these techniques cannot be expected to work away from half filling when the "sign problem" in quantum Monte Carlo simulations is present.

132 citations

Journal ArticleDOI
TL;DR: This work investigates several three-dimensional lattice models believed to be in the Ising universality class by means of Monte Carlo methods and finite-size scaling, and analyzes all the data simultaneously such that the universal parameters occur only once, leading to an improved accuracy.
Abstract: We investigate several three-dimensional lattice models believed to be in the Ising universality class by means of Monte Carlo methods and finite-size scaling. These models include spin- 1 models with nearestneighbor interactions on the simple-cubic and on the diamond lattice. For the simple cubic lattice, we also include models with third-neighbor interactions of varying strength, and some ‘‘equivalent-neighbor’’ models. Also included are a spin-1 model and a hard-core lattice gas. Separate analyses of the numerical data confirm the Ising-like critical behavior of these systems. On this basis, we analyze all these data simultaneously such that the universal parameters occur only once. This leads to an improved accuracy. The thermal, magnetic, and irrelevant exponents are determined as y t51.5868(3), y h52.4816(1), and y i520.821(5), respectively. The Binder ratio is estimated as Q5^m 2 & 2 /^m 4 &50.62 341(4).

132 citations

Journal ArticleDOI
TL;DR: In this article, a group theoretical method is presented for constructing new unitary representations of the Virasoro algebra out of Fermi fields and the critical exponents are calculated explicitly from the construction.

132 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023682
20221,314
2021854
2020947
2019870
2018844