/BitsPerComponent 8 endobj >> /R [46 27 302 739 ] At Tc this average correlation function behaves asympotically as N-2 (lnmN-2)-1 when m the separation between boundary spins, is large. III. 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). >> /Length 459 15 0 obj /R [46 27 302 739 ] /P 20 0 R /N 16 0 R Some applications, theorems and conjecturesAdv, Coherence and dissipative dynamics in the quantum brain model, The Theory and Application of Axial Ising Models, Ground-state statistics from annealing algorithms: Quantum versus classical approaches, On the Adiabatic Theorem of Quantum Mechanics, Entropy and correlation functions of a driven quantum spin chain, An inequality for positive linear integral operators, Image analysis, random fields and Markov chain Monte Carlo methods. >> in the Hopfield model in a transverse field in thermal equi-librium @5#. This work introduces these quantum Ising models and analyses them both theoretically and numerically in great detail. C: Solid State Phys. Active 7 months ago. temporär gesenkter USt. 6 0 obj /R [46 653 302 739 ] /R [310 27 566 739 ] >> 6 2459, https://doi.org/10.1088/0022-3719/6/15/009. After postdoctoral experience at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, and at Wuerzburg University, Germany, he joined the Indian Institute of Technology, Kanpur, in 2003, where he is currently a professor. The transverse field Ising and XY models (the simplest quantum spin models) provide the organising principle for the rich variety of interconnected subjects which are covered in this book. /V 28 0 R The Ising model is defined with the Hamiltonian: $$ H = -\sum_{}S_i^z\cdot S_j^z $$ What is the difference between quantum version and classical version? << antiferromagnets; 20. In this manner we obtain the T=0 result that if the interaction is stronger in the x direction, then rhoNx approaches a constant exponentially while rhoNy approaches zero exponentially as N-->∞. Other collective excitations resembling higher bound pair states may or may not exist but do not seriously affect the energy gap. Ihre zuletzt angesehenen Artikel und besonderen Empfehlungen. 19 0 obj Phase transitions of Dirac fermions; 18. >> /Gamma [1.8 1.8 1.8] We therefore discuss in this paper the transverse Ising model with a vari-ety of exchange interactions. 21 0 obj We finally show that in the isotropic case at T=0 that rhoNx=rhoNy-->N- 12. 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. /V 19 0 R /R [46 471 302 739 ] /P 17 0 R Finden Sie alle Bücher, Informationen zum Autor. 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. We modify the usual rectangular lattice by allowing each row of vertical bonds to vary randomly from row to row with a prescribed probability function. /N 10 0 R /N 36 0 R >> Title: Quantum Ising Model in an Alternating Transverse Field. 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. This is to be compared to increasing temperature in the classical Ising model, where it's thermal fluctuations that cause a classical phase transition from a ferromagnetic to a paramagnetic state. %PDF-1.1 Random quantum systems that exhibit unusual behavior associated with ``infinite randomness'' fixed points are discussed, focusing on the random quantum Ising model. Hinzufügen war nicht erfolgreich. Tables. For nonzero temperature we derive both low- and high-temperature expansions for all three correlations and show that these correlations go to zero exponentially as N-->∞. Furthermore, at Tc the average boundary magnetization behaves as -N-1 sign (H)[ln Nβc|H|]-1, where N-1 is a measure of the width of the distribution of random bonds. >> >> By continuing to use this site you agree to our use of cookies. 12 0 obj Published under licence by IOP Publishing Ltd Number 15, R B Stinchcombe 1973 J. Phys. >> Todos los derechos reservados. << I. gF/(+GaKo$qneLWDrQ#;5\S(\$q'LM9bYJX9N;hHO_e;>`Y"/'J:I~> << Spin Correlation Functions, Theory of a Two-Dimensional Ising Model with Random Impurities. /R [310 50 566 530 ] Fermi liquids, and in quantum information sciences. Further, it points to the obstacles still remaining to develop a successful quantum computer. Quantum spin glasses; References; /P 30 0 R These correlations are not probability-1 objects and have a probability distribution. 12. 2nd revised ed, On certain Hermitian forms associated with the Fourier series of a positive function, Integrals of motion and S-matrix of the (scaled) T = Tc Ising model with magnetic field, Quantum Mechanics: Non-Relativistic Theory, Correlation Index of the Ising Model with a Transverse Field, Scaling Theory for Finite-Size Effects in the Critical Region, On the p-spin interaction transverse Ising spin-glass model without replicas, Magnetic properties of a transverse spin-1 Ising model with random longitudinal field, Exact ground-state excitations of the XY model in a transverse field in one dimension, A study of the quenched diluted spin transverse Ising model, Quantum fluctuations in an ising spin glass with transverse field, Spin glass transition in an Ising spin system with transverse field, The anomalous schottky heat capacity of cerium ethylsulphate.

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