Find out more. II. Over 10 million scientific documents at your fingertips. Journal of Physics C: Solid State Physics, Spectral functions and damping, Thermal and magnetic properties of the transverse Ising model, The anisotropic Heisenberg ferromagnet with arbitrary field direction. Evidence for order-disorder character from greater entropy difference between ferro- electric and paraelectric phases add smaller Curie constant than in displacive ferroelectrics, such as double oxides with perovskite structure (Blinc and Svetina 1966a, b). Find out more about journal subscriptions at your site. For modeling purposes, most of the current innovative and successful research in this field has been obtained by either directly or indirectly using the insights provided by quantum (or transverse field) Ising models because of the separability of the cooperative interaction from the tunable transverse field or tunneling term in the relevant Hamiltonian. A brief review is first made of systems for which the spin-1/2 Ising model in a transverse field provides a useful description (insulating magnetic systems, order-disorder ferroelectrics, cooperative Jahn-Teller systems and other systems with 'pseudo-spin'- phonon interactions). More precisely, the symmetry transformation is given by the unitary $${\displaystyle \prod _{j}X_{j}}$$. Not logged in Also, a number of condensed matter systems can be modeled accurately in this approach, hence granting the possibility to compare advanced models with actual experimental results. 6 2459, https://doi.org/10.1088/0022-3719/6/15/009. I. Thermodynamics, The anisotropic Heisenberg ferromagnet with arbitrary field direction. Please choose one of the options below. Ising model in a transverse field: I. To gain access to this content, please complete the Recommendation The formalism, which is the first application of such techniques to systems with varying magnetization direction, provides a basis for subsequent higher-order calculations of the free energy and correlation functions. Lecture Notes in Physics © 2020 Springer Nature Switzerland AG. For modeling purposes, most of the current innovative and successful research in this field has been obtained by either directly or indirectly using the insights provided by quantum (or transverse field) Ising models because of the separability of the cooperative interaction from the tunable transverse field or tunneling term in the relevant Hamiltonian. For simplicity here $${\displaystyle X}$$ and $${\displaystyle Z}$$ are normalised to each have determinant -1. in quantum information sciences. Following the duality of the two dimensional Ising model on square lattice, one can show the self-duality, and thereby make exact estimate of the critical tunnelling (transverse) ﬁeld of the one-dimensional spin-1 / 2 transverse Ising model. Major advances have been made in both theoretical and experimental investigations of the nature and behavior of quantum phases and transitions in cooperatively interacting many-body quantum systems. Volume 6, If you have a user account, you will need to reset your password the next time you login. The computer you are using is not registered by an institution with a subscription to this article. This work introduces these quantum Ising models and analyses them both theoretically and numerically in great detail. book series RIS. it represents a spin 1/2 particle). The perturbation series is classified with respect to the small parameter 1/z, where z is the number of psins interacting with a given spin; this generates the molecular-field approximation and the random-phase approximation as the lowest-order description of the thermodynamic functions and correlation functions respectively. With its tutorial approach the book addresses above all young researchers who wish to enter the field and are in search of a suitable and self-contained text, yet it will also serve as a valuable reference work for all active researchers in this area. 108.179.209.90, Sei Suzuki, Jun-ichi Inoue, Bikas K. Chakrabarti, Cooperatively interacting many-body systems, Graduate School of Physics, and Mathematics, Centre for Applied Mathematics &, Computational Sciences, https://doi.org/10.1007/978-3-642-33039-1, Transverse Ising System in Higher Dimensions (Pure Systems), Dilute and Random Transverse Ising Systems, Transverse Ising Spin Glass and Random Field Systems.