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Theory of Critical Phenomena in Finite-size Systems

2000 Science
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Release : 2000
Genre : Science
Kind : eBook
Book Rating : 251/5 ( reviews)

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Book Synopsis Theory of Critical Phenomena in Finite-size Systems by : ?ordan Brankov

Download or read book Theory of Critical Phenomena in Finite-size Systems written by ?ordan Brankov. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveals the intimate mechanism of how the critical singularities build up in the thermodynamic limit; and (4) can be fruitfully used to explain the low-temperature behaviour of quantum critical systems. The exposition is given in a self-contained form which presumes the reader's knowledge only in the framework of standard courses on the theory of phase transitions and critical phenomena. The instructive role of simple models, both classical and quantum, is demonstrated by putting the accent on the derivation of rigorous and exact analytical results.

Finite-Size Scaling

2012-12-02 Computers
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Release : 2012-12-02
Genre : Computers
Kind : eBook
Book Rating : 062/5 ( reviews)

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Book Synopsis Finite-Size Scaling by : J. Cardy

Download or read book Finite-Size Scaling written by J. Cardy. This book was released on 2012-12-02. Available in PDF, EPUB and Kindle. Book excerpt: Over the past few years, finite-size scaling has become an increasingly important tool in studies of critical systems. This is partly due to an increased understanding of finite-size effects by analytical means, and partly due to our ability to treat larger systems with large computers. The aim of this volume was to collect those papers which have been important for this progress and which illustrate novel applications of the method. The emphasis has been placed on relatively recent developments, including the use of the &egr;-expansion and of conformal methods.

Quantum Field Theory and Critical Phenomena

2021 Science
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Release : 2021
Genre : Science
Kind : eBook
Book Rating : 624/5 ( reviews)

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Book Synopsis Quantum Field Theory and Critical Phenomena by : Jean Zinn-Justin

Download or read book Quantum Field Theory and Critical Phenomena written by Jean Zinn-Justin. This book was released on 2021. Available in PDF, EPUB and Kindle. Book excerpt: Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamics has been the first example of a Quantum Field Theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics. As this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale. Therefore, this text sets out to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group properties are systematically discussed. The notion of effective field theory and the emergence of renormalisable theories are described. The consequences for fine tuning and triviality issue are emphasized. This fifth edition has been updated and fully revised, e.g. in particle physics with progress in neutrino physics and the discovery of the Higgs boson. The presentation has been made more homogeneous througout the volume, and emphasis has been put on the notion of effective field theory and discussion of the emergence of renormalisable theories.

Quantum Scaling in Many-Body Systems

2017-04-17 Science
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Release : 2017-04-17
Genre : Science
Kind : eBook
Book Rating : 256/5 ( reviews)

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Book Synopsis Quantum Scaling in Many-Body Systems by : Mucio Continentino

Download or read book Quantum Scaling in Many-Body Systems written by Mucio Continentino. This book was released on 2017-04-17. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on experimental results, this updated edition approaches the problem of quantum phase transitions from a new and unifying perspective.

Quantum Scaling in Many-Body Systems

2017-04-17 Science
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Release : 2017-04-17
Genre : Science
Kind : eBook
Book Rating : 12X/5 ( reviews)

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Book Synopsis Quantum Scaling in Many-Body Systems by : Mucio Continentino

Download or read book Quantum Scaling in Many-Body Systems written by Mucio Continentino. This book was released on 2017-04-17. Available in PDF, EPUB and Kindle. Book excerpt: Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.

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