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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 paper, the non-linear equations of motion of classical antiferromagnetic chains in a continuum description are presented for isotropic exchange, various combinations of single-ion anisotropies (Ising and xy-like) and external magnetic fields (supporting and breaking the anisotropy).
Abstract: Solutions are presented to the non-linear equations of motion of classical antiferromagnetic chains in a continuum description. Results have been obtained for, in addition to isotropic exchange, various combinations of single-ion anisotropies (Ising and xy-like) and external magnetic fields (supporting and breaking the anisotropy). Among the solutions are both sine-Gordon solitons, representing antiferromagnetic domain walls and pulse solitons with continuously varying amplitude. Solitons in the xy antiferromagnet in asymmetry-breaking external field are discussed with respect to their observability in TMMC. They are found to contribute two different central peaks to the dynamical structure factor.

125 citations

Journal ArticleDOI
TL;DR: In this article, an extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimensionLαγγαβαγαγ βαγβ β β βαβ ββ βα ββαβββα β βββγ ββγββ βγβαα βααβγγβγα βγγγ βγααα αββδ ββλββλα βλαβλ
Abstract: Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponentsv ‖,v ⊥: uniaxial Lifshitz points, the Kawasaki spin exchange model driven by an electric field, etc. An extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimensionL ‖ in the special direction and linear dimensionsL ⊥ in all other directions. The related shape effects forL ‖≠L ⊥ but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relationv ‖+(d−1)v ⊥=γ+2β does not hold. As a test of these ideas, a Monte Carlo simulation study for shape effects at isotropic critical point in the two-dimensional Ising model is presented, considering subsystems of a 1024x1024 square lattice at criticality.

125 citations

Journal ArticleDOI
TL;DR: In this article, the authors show that confinement in the quantum Ising model leads to non-thermal eigenstates, in both continuum and lattice theories in both one (1D) and two dimensions (2D).
Abstract: We show that confinement in the quantum Ising model leads to nonthermal eigenstates, in both continuum and lattice theories, in both one (1D) and two dimensions (2D). In the ordered phase, the presence of a confining longitudinal field leads to a profound restructuring of the excitation spectrum, with the low-energy two-particle continuum being replaced by discrete “meson” modes (linearly confined pairs of domain walls). These modes exist far into the spectrum and are atypical, in the sense that expectation values in the state with energy E do not agree with the microcanonical (thermal) ensemble prediction. Single meson states persist above the two-meson threshold due to a surprising lack of hybridization with the (n ≥ 4)-domain wall continuum, a result that survives into the thermodynamic limit and that can be understood from analytical calculations. The presence of such states is revealed in anomalous postquench dynamics, such as the lack of a light cone, the suppression of the growth of entanglement entropy, and the absence of thermalization for some initial states. The nonthermal states are confined to the ordered phase—the disordered (paramagnetic) phase exhibits typical thermalization patterns in both 1D and 2D in the absence of integrability.

125 citations

Journal ArticleDOI
TL;DR: In this article, an identity on paths in planar graphs conjectured by Feynman [H] is rigorously established and a complete analysis of the combinatorial approach to the two-dimensional Ising model with nearest neighbor interaction and 0 external magnetic field is presented.
Abstract: An identity on paths in planar graphs conjectured by Feynman [H] is rigorously established. This permits a complete analysis of the combinatorial approach to the two‐dimensional Ising model with nearest neighbor interaction and 0 external magnetic field previously heuristically discussed by Kac and Ward [KW] and Potts and Ward [PW]. Relevant identities are established for the two‐dimensional Ising model with next nearest neighbor interactions and 0 external magnetic field, for the two‐dimensional Ising model with nearest neighbor interactions and positive external magnetic field, and for the three‐dimensional Ising model with nearest neighbor interactions and 0 external field. For the case of a square net with an odd number of spin locations with nearest neighbor interactions and external field equal to iπ/2, it is shown that the partition function is identically zero for both plane and torus imbedding contrary to a result announced by Lee and Yang [LY; Eq. (48)], which turns out to be correct only for an even number of spin locations.

125 citations

Journal ArticleDOI
TL;DR: In this article, the authors explore the dynamics of artificial one and two-dimensional Ising-like quantum antiferromagnets with different lattice geometries by using a Rydberg quantum simulator of up to 36 spins in which they dynamically tune the parameters of the Hamiltonian.
Abstract: We explore the dynamics of artificial one- and two-dimensional Ising-like quantum antiferromagnets with different lattice geometries by using a Rydberg quantum simulator of up to 36 spins in which we dynamically tune the parameters of the Hamiltonian. We observe a region in parameter space with antiferromagnetic (AF) ordering, albeit with only finite-range correlations. We study systematically the influence of the ramp speeds on the correlations and their growth in time. We observe a delay in their build-up associated to the finite speed of propagation of correlations in a system with short-range interactions. We obtain a good agreement between experimental data and numerical simulations taking into account experimental imperfections measured at the single particle level. Finally, we develop an analytical model, based on a short-time expansion of the evolution operator, which captures the observed spatial structure of the correlations, and their build-up in time.

125 citations


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