UID:
almafu_9960119224702883
Format:
1 online resource (xiv, 353 pages) :
,
digital, PDF file(s).
ISBN:
0-511-62254-6
Content:
Quantum Phase Transitions is the first book to describe in detail the fundamental changes that can occur in the macroscopic nature of matter at zero temperature due to small variations in a given external parameter. The subject plays a central role in the study of the electrical and magnetic properties of numerous important solid state materials. The author begins by developing the theory of quantum phase transitions in the simplest possible class of non-disordered, interacting systems - the quantum Ising and rotor models. Particular attention is paid to their non-zero temperature dynamic and transport properties in the vicinity of the quantum critical point. Several other quantum phase transitions of increasing complexity are then discussed and clarified. Throughout, the author interweaves experimental results with presentation of theoretical models, and well over 500 references are included. The book will be of great interest to graduate students and researchers in condensed matter physics.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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Cover -- Frontmatter -- Contents -- Preface -- Acknowledgments -- Introduction -- Basic Concepts -- 1.1 What Is a Quantum Phase Transition? -- 1.2 Quantum Versus Classical Phase Transitions -- 1.3 Experimental Examples -- 1.4 Theoretical Models -- The Mapping to Classical Statistical Mechanics: Single-Site Models -- 2.1 The Classical Ising Chain -- 2.2 The Classical XY Chain and an O(2) Quantum Rotor -- 2.3 The Classical Heisenberg Chain and an O(3) Quantum Rotor -- Overview -- 3.1 Quantum Field Theories -- 3.2 What's Different about Quantum Transitions? -- Quantum Ising and Rotor Models -- The Ising Chain in a Transverse Field -- 4.1 Limiting Cases at T = 0 -- 4.2 Exact Spectrum -- 4.3 Continuum Theory and Scaling Transformations -- 4.4 Equal-Time Correlations of the Order Parameter -- 4.5 Finite-Temperature Crossovers -- 4.6 Applications and Extensions -- Quantum Rotor Models: Large-N Limit -- 5.1 Limiting Cases -- 5.2 Continuum Theory and Large-N Limit -- 5.3 Zero Temperature -- 5.4 Nonzero Temperatures -- 5.5 Applications and Extensions -- The d = 1, O(N ≥ 3) Rotor Models -- 6.1 Scaling Analysis at Zero Temperature -- 6.2 Low-Temperature Limit of Continuum Theory, T ≪ Δ+ -- 6.3 High-Temperature Limit of Continuum Theory, Δ+ ≪ T ≪ J -- 6.4 Summary -- 6.5 Applications and Extensions -- The d = 2, O(N ≥ 3) Rotor Models -- 7.1 Low T on the Magnetically Ordered Side, T ≪ ρs -- 7.2 Dynamics of the Quantum Paramagnetic and High-T Regions -- 7.3 Summary -- 7.4 Applications and Extensions -- Physics Close to and above the Upper-Critical Dimension -- 8.1 Zero Temperature -- 8.2 Statics at Nonzero Temperatures -- 8.3 Order Parameter Dynamics in d = 2 -- 8.4 Applications and Extensions -- Transport in d = 2 -- 9.1 Perturbation Theory -- 9.2 Collisionless Transport Equations -- 9.3 Collision-Dominated Transport -- 9.4 Physical Interpretation.
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9.5 Applications and Extensions -- Other Models -- Boson Hubbard Model -- 10.1 Mean-Field Theory -- 10.2 Continuum Quantum Field Theories -- 10.3 Applications and Extensions -- Dilute Fermi and Bose Gases -- 11.1 The Quantum X X Model -- 11.2 The Dilute Spinless Fermi Gas -- 11.3 The Dilute Bose Gas -- 11.4 Correlators of ZB in d = 1 -- 11.5 Applications and Extensions -- Phase Transitions of Fermi Liquids -- 12.1 Effective Field Theory -- 12.2 Finite-Temperature Crossovers -- 12.3 Applications and Extensions -- Heisenberg Spins: Ferromagnets and Antiferromagnets -- 13.1 Coherent State Path Integral -- 13.2 Quantized Ferromagnets -- 13.3 Antiferromagnets -- 13.4 Partial Polarization and Canted States -- 13.5 Applications and Extensions -- Spin Chains: Bosonization -- 14.1 The X X Chain Revisited: Bosonization -- 14.2 Phases of H12 -- 14.3 O(2) Rotor Model in d = 1 -- 14.4 Applications and Extensions -- Magnetic Ordering Transitions of Disordered Systems -- 15.1 Stability of Quantum Critical Points in Disordered Systems -- 15.2 Griffiths-McCoy Singularities -- 15.3 Perturbative Field-Theoretic Analysis -- 15.4 Quantum Ising Models Near the Percolation Transition -- 15.5 The Disordered Quantum Ising Chain -- 15.6 Discussion -- 15.7 Applications and Extensions -- Quantum Spin Glasses -- 16.1 The Effective Action -- 16.2 Mean-Field Theory -- 16.3 Applications and Extensions -- References -- Index.
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English
Additional Edition:
ISBN 0-521-00454-3
Additional Edition:
ISBN 0-521-58254-7
Language:
English
URL:
https://doi.org/10.1017/CBO9780511622540
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