Introduction To The Theory Of Critical Phenomena
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The Theory Of Critical Phenomena
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Author :
language : en
Publisher: Oxford University Press
Release Date : 1992-06-11
The Theory Of Critical Phenomena written by and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-06-11 with Science categories.
The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.
A Primer To The Theory Of Critical Phenomena
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Author : Jurgen M. Honig
language : en
Publisher: Elsevier
Release Date : 2018-02-05
A Primer To The Theory Of Critical Phenomena written by Jurgen M. Honig and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Science categories.
A Primer to the Theory of Critical Phenomena provides scientists in academia and industry, as well as graduate students in physics, chemistry, and geochemistry with the scientific fundamentals of critical phenomena and phase transitions. The book helps readers broaden their understanding of a field that has developed tremendously over the last forty years. The book also makes a great resource for graduate level instructors at universities. - Provides a thorough and accessible treatment of the fundamentals of critical phenomena - Offers an in-depth exposition on renormalization and field theory techniques - Includes experimental observations of critical effects - Includes live examples illustrating the applications of the theoretical material
Introduction To The Theory Of Critical Phenomena
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Author : Dimo I. Uzunov
language : en
Publisher: World Scientific
Release Date : 2010
Introduction To The Theory Of Critical Phenomena written by Dimo I. Uzunov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.
Introduction To Conformal Invariance And Its Applications To Critical Phenomena
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Author : Philippe Christe
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-04-13
Introduction To Conformal Invariance And Its Applications To Critical Phenomena written by Philippe Christe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-13 with Science categories.
The history of critical phenomena goes back to the year 1869 when Andrews discovered the critical point of carbon dioxide, located at about 31°C and 73 atmospheres pressure. In the neighborhood ofthis point the carbon dioxide was observed to become opalescent, that is, light is strongly scattered. This is nowadays interpreted as comingfrom the strong fluctuations of the system close to the critical point. Subsequently, a wide varietyofphysicalsystems were realized to display critical points as well. Ofparticular importance was the observation of a critical point in ferromagnetic iron by Curie. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and may even extend to the quark-gluon plasmaand the early universe as a whole. Early theoretical investigationstried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations and culminating in Landau's general theory of critical phenomena. In a dramatic development, Onsager's exact solutionofthe two-dimensional Ising model made clear the important role of the critical fluctuations. Their role was taken into account in the subsequent developments leading to the scaling theories of critical phenomena and the renormalization group. These developements have achieved a precise description of the close neighborhood of the critical point and results are often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is today emphasized.
Theory Of Critical Phenomena In Finite Size Systems Scaling And Quantum Effects
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Author : Jordan G Brankov
language : en
Publisher: World Scientific
Release Date : 2000-08-21
Theory Of Critical Phenomena In Finite Size Systems Scaling And Quantum Effects written by Jordan G Brankov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-21 with Science categories.
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.
Introduction To The Theory Of Critical Phenomena Mean Field Fluctuations And Renormalization
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Author : Dimo I Uzunov
language : en
Publisher: World Scientific
Release Date : 1993-03-09
Introduction To The Theory Of Critical Phenomena Mean Field Fluctuations And Renormalization written by Dimo I Uzunov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-09 with Science categories.
The sophistication of modern tools used in the study of statistical mechanics and field theory is often an obstacle to the easy understanding of new important current results reported in journals. The main purpose of this book is to introduce the reader to the methods of the fluctuation (field) theory of phase transitions and critical phenomena so as to provide a good source for research. The introductory contents are concerned with ideas of description, thermodynamic stability theory related to phase transitions, major experimental facts, basic models and their relationships. Special attention is paid to the mean field approximation and to the Landau expansion for simple and complex models of critical and multicritical phenomena. An instructive representation of the modern perturbation theory and the method of the renormalization group is developed for field models of phase transitions. The essential influence of the fluctuations on the critical behaviour is established together with the theory of correlation functions, Gaussian approximation, the Ginzburg criterion, ∈- and 1/n- expansions as practical realizations of the renormalization group ideas. Applications of the theory to concrete aspects of condensed matter physics are considered: quantum effects, Bose condensation, crystal anisotropy, superconductors and liquid crystals, effects of disorder of type randomly distributed quenched impurities and random fields. This volume can be used as an advanced University course book for students with a basic knowledge of statistical physics and quantum mechanics. It could be considered as a complementary text to a standard University course on statistical physics.
Introduction To The Theory Of Critical Phenomena
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Author : Dimo I. Uzunov
language : en
Publisher:
Release Date : 2010
Introduction To The Theory Of Critical Phenomena written by Dimo I. Uzunov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Electronic books categories.
Elements Of Phase Transitions And Critical Phenomena
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Author : Hidetoshi Nishimori
language : en
Publisher: Oxford University Press
Release Date : 2011
Elements Of Phase Transitions And Critical Phenomena written by Hidetoshi Nishimori and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.
Quantum Field Theory And Critical Phenomena
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Author : Jean Zinn-Justin
language : en
Publisher: Oxford University Press, USA
Release Date : 1993
Quantum Field Theory And Critical Phenomena written by Jean Zinn-Justin and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Language Arts & Disciplines categories.
Describes particle physics and critical phenomena in statistical mechanics in a unified framework, incorporating graduate lecture notes from the 1970s and 1980s at several universities in Europe and the US. Deals with general field theory, functional integrals, and functional methods; renormalization properties of theories with symmetries and specific applications to particle physics; lattice gauge theories and asymptotic freedom in four dimensions; and the role of instantons and the application of instanton calculus to the large-order behavior of perturbation theory and the problem of summation of the perturbative expansion. Several chapters close with exercise, solutions or hints for which are provided. No dates are noted for the previous editions. Annotation copyright by Book News, Inc., Portland, OR
Critical Phenomena In Natural Sciences
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Author : Didier Sornette
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Critical Phenomena In Natural Sciences written by Didier Sornette and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. This is the first textbook written by a well-known expert that provides a modern up-to-date introduction for workers outside statistical physics. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to post-docs in geophysics and meteorology.