Quantum Ising phases and transitions in transverse Ising models
type: Item
instance of: scholarly article
title: Quantum Ising phases and transitions in transverse Ising models
zbMATH Open document ID: 1268.82001
DOI: 10.1007/978-3-642-33039-1
author: Sei Suzuki
author: Jun-Ichi Inoue
author: Bikas. K. Chakrabarti
published in: Lecture Notes in Physics
publication date: 2012-12-27T00:00:00Z
review text: The book introduces quantum Ising models and analyses them theoretically and numerically. It discusses both the static and the dynamic behavior of the pure and disordered models, including quantum annealing phenomena. The book consists of eleven chapters. Chapter 1 gives a general introduction to transverse Ising models and their relevance in the context of modeling various quantum order-disorder transitions. In Chapter 2, the energy spectrum of pure transverse Ising chains is discussed. One of the peculiarity of transverse Ising models is the solvability of the pure transverse Ising chain. The exact solution using the Jordan-Wigner transformation is presented. This chapter also includes several numerical analytic methods. In Chapter 3, the Suzuki-Trotter mapping of the \(d\)-dimensional quantum Ising systems to the \((d+1)\)-dimensional classical Ising systems is discussed. Various approximate analytical methods are discussed to study the behavior of the transverse Ising and other generalized models, employing scaling theory and both real space and field theoretical renormalization group techniques. In Chapter 4, the behavior of regularly frustrated transverse Ising systems is discussed. In Chapter 5, the behavior of randomly dilute Ising systems in transverse fields is discussed. Detailed analytical and numerical results revealing the nature of the possible disordered Griffiths phase and its singularities are presented. Chapter 6 presents the behavior of randomly frustrated transverse Ising spin glasses and also of random field transverse Ising models. Chapter 7 discusses the dynamics of quantum transverse Ising models without disorder or frustration and in particular for quenching through the critical point. In Chapter 8, quantum annealing techniques and results are presented. Several analytical results on the bounds of search times and numerical techniques and results for annealing are given. Chapter 9 discusses some applications of tuning quantum fluctuations i…
Mathematics Subject Classification ID: 82-02
Mathematics Subject Classification ID: 82B26
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 82B28
zbMATH DE Number: 6118251
zbMATH Keywords: quantum Ising model
zbMATH Keywords: phase
zbMATH Keywords: transverse Ising model
zbMATH Keywords: disordered model
zbMATH Keywords: spectrum
Wikidata QID: Q56212865
reviewed by: U. A. Rozikov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-33039-1
OpenAlex ID: W4230053572
description: scientific article; zbMATH DE number 6118251