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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: The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe observables in isolated integrable quantum systems after equilibration as mentioned in this paper, and it has been demonstrated to be a powerful tool to predict the outcome of the relaxation dynamics of few-body observables.
Abstract: The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe observables in isolated integrable quantum systems after equilibration. Since then, the GGE has been demonstrated to be a powerful tool to predict the outcome of the relaxation dynamics of few-body observables in a variety of integrable models, a process we call generalized thermalization. This review discusses several fundamental aspects of the GGE and generalized thermalization in integrable systems. In particular, we focus on questions such as: which observables equilibrate to the GGE predictions and who should play the role of the bath; what conserved quantities can be used to construct the GGE; what are the differences between generalized thermalization in noninteracting systems and in interacting systems mappable to noninteracting ones; why is it that the GGE works when traditional ensembles of statistical mechanics fail. Despite a lot of interest in these questions in recent years, no definite answers have been given. We review results for the XX model and for the transverse field Ising model. For the latter model, we also report original results and show that the GGE describes spin-spin correlations over the entire system. This makes apparent that there is no need to trace out a part of the system in real space for equilibration to occur and for the GGE to apply. In the past, a spectral decomposition of the weights of various statistical ensembles revealed that generalized eigenstate thermalization occurs in the XX model (hard-core bosons). Namely, eigenstates of the Hamiltonian with similar distributions of conserved quantities have similar expectation values of few-spin observables. Here we show that generalized eigenstate thermalization also occurs in the transverse field Ising model.

371 citations

Journal ArticleDOI
TL;DR: In this paper, a renormalization group transformation is introduced with the help of which critical properties of infinite systems can be related to finite systems, and applied to the two-dimensional Ising model.
Abstract: A renormalization group transformation is introduced with the help of which critical properties of infinite systems can be related to finite systems. As a numerical example the method is applied to the two-dimensional Ising model. The critical point and critical point exponent are computed in addition to the amplitude of the logarithmic singularity in the specific heat.

370 citations

Journal ArticleDOI
TL;DR: In this paper, the entanglement entropy of two disjoint intervals in conformal field theories was studied and the scaling function for small four-point ratio (i.e. short intervals) was given.
Abstract: We continue the study of the entanglement entropy of two disjoint intervals in conformal field theories that we started in J. Stat. Mech. (2009) P11001. We compute Tr\rho_A^n for any integer n for the Ising universality class and the final result is expressed as a sum of Riemann-Siegel theta functions. These predictions are checked against existing numerical data. We provide a systematic method that gives the full asymptotic expansion of the scaling function for small four-point ratio (i.e. short intervals). These formulas are compared with the direct expansion of the full results for free compactified boson and Ising model. We finally provide the analytic continuation of the first term in this expansion in a completely analytic form.

367 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the field theory describing the scaling limit of T = Tc Ising model with nonzero magnetic field possesses a number of nontrivial local integrals of motion.
Abstract: It is shown that the field theory describing the scaling limit of T = Tc Ising model with nonzero magnetic field possesses a number of nontrivial local integrals of motion. The exact mass spectrum and S-matrix of this field theory is conjectured.

366 citations

Journal ArticleDOI
TL;DR: In this paper, the Schrodinger invariance criterion for strongly anisotropic or dynamical scaling to local scale invariance is investigated, and a simple scaling form of the two-point function close to a free surface which can be either spacelike or timelike.
Abstract: The extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated. For the special case of an anisotropy or dynamical exponent θ=z=2, the group of local scale transformation considered is the Schrodinger group, which can be obtained as the nonrelativistic limit of the conformal group. The requirement of Schrodinger invariance determines the two-point function in the bulk and reduces the three-point function to a scaling form of a single variable. Scaling forms are also derived for the two-point function close to a free surface which can be either spacelike or timelike. These results are reproduced in several exactly solvable statistical systems, namely the kinetic Ising model with Glauber dynamics, lattice diffusion, Lifshitz points in the spherical model, and critical dynamics of the spherical model with a nonconserved order parameter. For generic values of θ, evidence from higher-order Lifshitz points in the spherical model and from directed percolation suggests a simple scaling form of the two-point function.

365 citations


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