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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: This work investigates and measures dynamical quantum phase transitions in a string of ions simulating interacting transverse-field Ising models, and establishes a link between DQPTs and the dynamics of other quantities such as the magnetization.
Abstract: The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.

457 citations

Journal ArticleDOI
TL;DR: In this paper, the equality of two critical points -the percolation threshold pH and the point pτ where the cluster size distribution ceases to decay exponentially -is proven for all translation invariant independent per-colation models on homogeneous d-dimensional lattices.
Abstract: The equality of two critical points - the percolation threshold pH and the point pτ where the cluster size distribution ceases to decay exponentially - is proven for all translation invariant independent percolation models on homogeneous d-dimensional lattices (d^ 1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameter M(β, h\ which for h = Q reduces to the percolation density P^ - at the bond density p = l—e~β in the single parameter case. These are: (1) M^hdM/dh + M2 + βMdM/dβ, and (2) dM/dβ^\J\MdM/dh. Inequality (1) is intriguing in that its derivation provides yet another hint of a "φ3 structure" in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents β and δ. One of these resembles an Ising model inequality of Frόhlich and Sokal and yields the mean field bound (5^2, and the other implies the result of Chayes and Chayes that β^ί. An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation /?((5 —1)^1 and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.

457 citations

Journal ArticleDOI
TL;DR: In this article, the authors review the quantum fidelity approach to quantum phase transitions in a pedagogical manner, and relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena.
Abstract: We review the quantum fidelity approach to quantum phase transitions in a pedagogical manner. We try to relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena. The definition of the fidelity and the scaling behavior of its leading term, as well as their explicit applications to the one-dimensional transverse-field Ising model and the Lipkin–Meshkov–Glick model, are introduced at the graduate-student level. Besides, we survey also other types of fidelity approach, such as the fidelity per site, reduced fidelity, thermal-state fidelity, operator fidelity, etc; as well as relevant works on the fidelity approach to quantum phase transitions occurring in various many-body systems.

456 citations

Journal ArticleDOI
TL;DR: In this article, the diffusion constant of spins in ferromagnets or of molecules in binary mixtures near the critical point is discussed employing a time-dependent Ising model in which spin interactions are replaced by certain temperature-dependent transition probabilities of spin exchange.
Abstract: The diffusion constant of spins in ferromagnets or of molecules in binary mixtures near the critical point is discussed employing a time-dependent Ising model in which spin interactions are replaced by certain temperature-dependent transition probabilities of spin exchange. The spin diffusion constant is calculated with the single approximation of replacing a reduced spin distribution function by its value for local equilibrium with a given inhomogeneous spin density. The behavior of the diffusion constant near the critical point is dominated by a factor ${\ensuremath{\chi}}^{\ensuremath{-}1}$, where $\ensuremath{\chi}$ is the magnetic susceptibility. This problem is also studied with the use of the Bethe lattice. The effects of surrounding spins on the transition probability for spin exchange are found to be essential for obtaining the critical slowing-down near the critical point. In view of this, Koci\ifmmode \acute{n}\else \'{n}\fi{}ski's calculation of the spin diffusion constant is critically discussed.

454 citations

Journal ArticleDOI
TL;DR: For random-field models, this work rigorously proves uniqueness of the Gibbs state 2D Ising systems, and absence of continuous symmetry breaking in the Heisenberg model in d\ensuremath{\le}4, as predicted by Imry and Ma.
Abstract: It is shown, by a general argument, that in 2D quenched randomness results in the elimination of discontinuities in the density of the thermodynamic variable conjugate to the fluctuating parameter. Analogous results for continuous symmetry breaking extend to d\ensuremath{\le}4. In particular, for random-field models we rigorously prove uniqueness of the Gibbs state 2D Ising systems, and absence of continuous symmetry breaking in the Heisenberg model in d\ensuremath{\le}4, as predicted by Imry and Ma. Another manifestation of the general statement is found in 2D random-bond Potts models where a phase transition persists, but ceases to be first order.

453 citations


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