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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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Book ChapterDOI
01 Jan 1989
TL;DR: In this article, the scaling limit of the Ising model with non-vanishing magnetic field was shown to have a non-trivial local integrals of motion, and the exact S-matrix for the critical Ising Model with magnetic field is conjectured.
Abstract: Equations of motion for two-dimensional quantum field theory obtained as some relevant perturbation around CFT are analyzed. It is shown that for particular degenerate fields taken as the perturbations, the resulting field theories posseses non-trivial local integrals of motion. The example is the scaling limit of the Ising model at $T = T_c$ but with non-vanishing magnetic field. Implications of the integrals of motion for corresponding particle theory are discussed and the exact S-matrix for the critical Ising model with magnetic field is conjectured.

425 citations

Journal ArticleDOI
TL;DR: In this paper, a quasiparticle theory for a single hole in a quantum antiferromagnet in the limit that the Heisenberg exchange energy is much less than the hopping matrix element, J\ensuremath{\ll}t.
Abstract: We formulate a quasiparticle theory for a single hole in a quantum antiferromagnet in the limit that the Heisenberg exchange energy is much less than the hopping matrix element, J\ensuremath{\ll}t. We consider the ground state of the spins to be either a quantum N\'eel state or a d-wave resonating-valence-bond (RVB) state. We show in a self-consistent perturbation theory that the hole spectrum is strongly renormalized by the interactions with spin excitations. The hole can be described by a narrow quasiparticle band located at an energy of order -t with a quasiparticle residue of order J/t and a bandwidth of order J. Above the quasiparticle band is an incoherent band of width of order t. Our results indicate that the energy scale for any coherent phenomenon involving the holes is \ensuremath{\delta}J, where \ensuremath{\delta} is the doping concentration. In the N\'eel state we perform a spin-wave expansion on an anisotropic Heisenberg model. In the Ising limit we reproduce previously known results and then expand perturbatively about that limit. In this expansion we find that the holes have a quasiparticle residue of ${J}_{z}$/t and a bandwidth of ${J}_{\ensuremath{\perp}}$. In the Heisenberg limit we employ a ``dominant pole'' approximation in which we ignore contributions to the self-energy from the incoherent part of the hole spectrum. A similar technique is used to study the d-wave RVB state. The relevance of our results to recent optical experiments is discussed.

425 citations

Book
23 Apr 2010
TL;DR: In this article, a detailed introduction to the ergodic theory of equilibrium states giving equal weight to two of its most important applications, namely to equilibrium statistical mechanics on lattices and to (time discrete) dynamical systems.
Abstract: This book provides a detailed introduction to the ergodic theory of equilibrium states giving equal weight to two of its most important applications, namely to equilibrium statistical mechanics on lattices and to (time discrete) dynamical systems. It starts with a chapter on equilibrium states on finite probability spaces which introduces the main examples for the theory on an elementary level. After two chapters on abstract ergodic theory and entropy, equilibrium states and variational principles on compact metric spaces are introduced emphasizing their convex geometric interpretation. Stationary Gibbs measures, large deviations, the Ising model with external field, Markov measures, Sinai-Bowen-Ruelle measures for interval maps and dimension maximal measures for iterated function systems are the topics to which the general theory is applied in the last part of the book. The text is self contained except for some measure theoretic prerequisites which are listed (with references to the literature) in an appendix.

422 citations

Journal ArticleDOI
TL;DR: In this paper, the scaling dimensions and OPE coefficients of the 3D Ising model were determined for O(2), O(3) and O(4) models from the conformal bootstrap with mixed correlators.
Abstract: We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coefficients obtained for the 3d Ising model, (Δ σ , Δ ϵ , λ σσϵ , λ ϵϵϵ ) = (0.5181489(10), 1.412625(10), 1.0518537(41), 1.532435(19) , give the most precise determinations of these quantities to date.

422 citations

Journal ArticleDOI
TL;DR: In this article, the phase diagram of strongly interacting matter as a function of temperature and baryon number density is explored, using a class of models for two-flavor QCD in which the interaction between quarks is modelled by that induced by instantons.

422 citations


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