Scaling and Renormalization in Statistical Physics


Author: John Cardy
Publisher: Cambridge University Press
ISBN: 9780521499590
Category: Science
Page: 238
View: 1519

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A thoroughly modern graduate-level introduction to the theory of critical behaviour. Covers phase transitions, mean field theory, phase diagrams, fixed points, cross-over behaviour, finite-size scaling, a simple approach to the epsilon expansion, low-dimensional systems, surface critical behaviour, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. Includes many problems.

Statistical Physics

Fundamentals and Application to Condensed Matter
Author: Hung T Diep
Publisher: World Scientific Publishing Company
ISBN: 9814696277
Category: Science
Page: 648
View: 1509

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The aim of this book is to provide the fundamentals of statistical physics and its application to condensed matter. The combination of statistical mechanics and quantum mechanics has provided an understanding of properties of matter leading to spectacular technological innovations and discoveries in condensed matter which have radically changed our daily life. The book gives the steps to follow to understand fundamental theories and to apply these to real materials.

Introduction to the Functional Renormalization Group


Author: Peter Kopietz,Lorenz Bartosch,Florian Schütz
Publisher: Springer Science & Business Media
ISBN: 364205093X
Category: Science
Page: 380
View: 5779

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This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.

Computational statistical physics

Lecture Notes, Guwahati SERC School
Author: Sitangshu Bikas Santra,Purusattam Ray
Publisher: Springer
ISBN: 9386279509
Category: Science
Page: 298
View: 2104

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The present book is an outcome of the SERC school on Computational Statistical Physics held at the Indian Institute of Technology, Guwahati, in December 2008. Numerical experimentation has played an extremely important role in statistical physics in recent years. Lectures given at the School covered a large number of topics of current and continuing interest. Based on lectures by active researchers in the field- Bikas Chakrabarti, S Chaplot, Deepak Dhar, Sanjay Kumar, Prabal Maiti, Sanjay Puri, Purusattam Ray, Sitangshu Santra and Subir Sarkar- the nine chapters comprising the book deal with topics that range from the fundamentals of the field, to problems and questions that are at the very forefront of current research. This book aims to expose the graduate student to the basic as well as advanced techniques in computational statistical physics. Following a general introduction to statistical mechanics and critical phenomena, the various chapters cover Monte Carlo and molecular dynamics simulation methodology, along with a variety of applications. These include the study of coarsening phenomena and diffusion in zeolites. /p In addition, graphical enumeration techniques are covered in detail with applications to percolation and polymer physics, and methods for optimisation are also discussed. Beginning graduate students and young researchers in the area of statistical physics will find the book useful. In addition, this will also be a valuable general reference for students and researchers in other areas of science and engineering.

Statistical Physics of Non-Thermal Phase Transitions

From Foundations to Applications
Author: Sergey G. Abaimov
Publisher: Springer
ISBN: 3319124692
Category: Science
Page: 497
View: 1935

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This book addresses the application of methods used in statistical physics to complex systems—from simple phenomenological analogies to more complex aspects, such as correlations, fluctuation-dissipation theorem, the concept of free energy, renormalization group approach and scaling. Statistical physics contains a well-developed formalism that describes phase transitions. It is useful to apply this formalism for damage phenomena as well. Fractals, the Ising model, percolation, damage mechanics, fluctuations, free energy formalism, renormalization group, and scaling, are some of the topics covered in Statistical Physics of Phase Transitions.

Statistical Physics of Particles


Author: Mehran Kardar
Publisher: Cambridge University Press
ISBN: 1139464876
Category: Science
Page: N.A
View: 2056

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Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.

Principles of Phase Structures in Particle Physics


Author: Hildegard Meyer-Ortmanns,Thomas Reisz
Publisher: World Scientific Publishing Company Incorporated
ISBN: N.A
Category: Science
Page: 682
View: 7337

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10(-10) sec after the big bang, when the universe cooled down to the order of 1015 Kelvin, the electroweak phase transition led to a spontaneous breaking of the symmetry between electromagnetic and weak interactions. 10(-6) sec later, at a temperature of the order of tera degrees, the QCD transition confined the free quarks and gluons to mesons and baryons in the hadronic phase of the present world. This book is about the analytical and numerical methods used to investigate these transitions within the framework of quantum field theory at finite temperature in a continuum formulation and on the lattice. The topics covered include the renormalization group approach in a perturbative and non-perturbative realization, dimensional reduction, asymptotic and convergent expansions in quantities such as strong and weak couplings, high temperatures, and small momenta. One particular case revolves around computer-aided generations of high-order hopping parameter series.

Physical Review

Statistical physics, plasmas, fluids, and related interdisciplinary topics. E
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Fluids
Page: N.A
View: 1955

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Hochenergiephysik


Author: Erich Lohrmann
Publisher: Springer-Verlag
ISBN: 332291805X
Category: Technology & Engineering
Page: 253
View: 7920

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Grundbegriffe der Wahrscheinlichkeitsrechnung


Author: A. Kolomogoroff
Publisher: Springer-Verlag
ISBN: 3642498884
Category: Mathematics
Page: 62
View: 501

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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Non-equilibrium Statistical Mechanics and Turbulence


Author: John Cardy,Gregory Falkovich,Krzysztof Gawedzki
Publisher: Cambridge University Press
ISBN: 9780521715140
Category: Mathematics
Page: 161
View: 7909

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This self-contained volume introduces modern methods of statistical mechanics in turbulence, with three harmonised lecture courses by world class experts.

Theorie der Wärme


Author: Richard Becker
Publisher: Springer-Verlag
ISBN: 3662249278
Category: Science
Page: 320
View: 777

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Schon seit langem wurde RICHARD BECKER von Freunden, Schülern und Kollegen bestürmt, seine "Theorie der Wärme" zu schreiben. Gerade diesem Gebiet hatte er seine Liebe und Aufmerksamkeit zugewandt. Das hat wohl daran gelegen, daß hier die Verflechtung des experimentellen Tatbestandes mit theoretischen Gedankengängen besonders innig ist und man daher den gesunden physikalischen Menschenverstand in besonderem Maße benötigt. Diese Art Physik lag ihm sehr und hier fühlte er sich zu Hause. Seine Vor lesungen über Wärme waren berühmt, und so entstand der berechtigte Wunsch, seine Art der Darstellung auch schwarz auf weiß zu besitzen. Nach langem Zureden hat RICHARD BECKER sich endlich vor etwa 5 Jah ren dazu entschlossen. Der Grundriß war bald aufgestellt, aber die Bearbei tung im einzelnen kostete viel Zeit und Mühe. Es war weniger das Auf schreiben und die Formulierung der Tatbestände, die Mühe machte. Das war ofl: genug eine Kleinigkeit. Meist aber gefiel ihm dann die eigene Darstellung nicht mehr. Es war ihm nicht klar, nicht anschaulich, nicht pointiert genug. Und dann wurde umgearbeitet, neu überlegt, zur Probe an der Tafel erzählt, so lange, bis es ihm wieder gefiel. Jeder Gedanke in diesem Buch ist so nach den verschiedensten Richtungen hin neu überlegt, verworfen und wieder aufgenommen worden. Auch als die erste Korrektur schon im Druck vorlag, gefiel ihm wieder manches nicht mehr, aber da war es zu spät. So reifl:e das Werk unter manch heimlichem Seufzer seiner Mitarbeiter heran und war Ende 1954 druckfertig.