Fields, Strings and Critical Phenomena
Fields, Strings and Critical Phenomena

Author: E. Brézin

Publisher: Elsevier Science & Technology

Published: 1990

Total Pages: 678

ISBN-13:

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Hardbound. This session of the Summer School in Theoretical Physics concentrated on the recent advances in areas of physics ranging from (super)strings to field theory and statistical mechanics. The articles contained in this volume provide a stimulating and up-to-date account of a rapidly growing subject.Discussion focussed on the many points of convergence between field theory and statistical mechanics: conformal field theory, field theory on a lattice, the study of strongly correlated electron systems, as in the Hubbard model, leading to topological Lagrangians, which are perhaps the key of the understanding of high Tc superconductivity or the fractional quantum Hall effect. The critical phenomena in (1+1) dimensions, in the domain in which quantum fluctuations are strong, are described for antiferromagnetic couplings by relativistic theories in which the methods of abelian or non-abelian bosonization are particularly powerful.

Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory
Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory

Author: Roberto Fernandez

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 446

ISBN-13: 3662028662

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Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.

Gauge Fields and Strings
Gauge Fields and Strings

Author: Polyakov

Publisher: Routledge

Published: 2018-05-02

Total Pages: 316

ISBN-13: 1351446088

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Based on his own work, the author synthesizes the most promising approaches and ideals in field theory today. He presents such subjects as statistical mechanics, quantum field theory and their interrelation, continuous global symmetry, non-Abelian gauge fields, instantons and the quantam theory of loops, and quantum strings and random surfaces. This book is aimed at postgraduate students studying field theory and statistical mechanics, and for research workers in continuous global theory.

Quantum Field Theory and Critical Phenomena
Quantum Field Theory and Critical Phenomena

Author: Jean Zinn-Justin

Publisher: Oxford University Press

Published: 2021-04-15

Total Pages: 1100

ISBN-13: 0192571613

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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.

Conformal Invariance And Applications To Statistical Mechanics
Conformal Invariance And Applications To Statistical Mechanics

Author: C Itzykson

Publisher: World Scientific

Published: 1998-09-29

Total Pages: 992

ISBN-13: 9814507598

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This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions.

From Fields To Strings: Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection (In 3 Vols)
From Fields To Strings: Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection (In 3 Vols)

Author: Shifman Misha

Publisher: World Scientific

Published: 2005-02-03

Total Pages: 2388

ISBN-13: 9814482048

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This volume is a collection of dedicated reviews covering all aspects of theoretical high energy physics and some aspects of solid state physics. Some of the papers are broad reviews of topics that span the entire field while others are surveys of authors' personal achievements. This is the most comprehensive review collection reflecting state of the art at the end of 2004. An important and unique aspect is a special effort the authors have invested in making the presentation pedagogical.

Conformal Invariance and Critical Phenomena
Conformal Invariance and Critical Phenomena

Author: Malte Henkel

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 433

ISBN-13: 3662039370

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Critical phenomena arise in a wide variety of physical systems. Classi cal examples are the liquid-vapour critical point or the paramagnetic ferromagnetic transition. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and fully developed tur bulence and may even extend to the quark-gluon plasma and the early uni verse as a whole. Early theoretical investigators tried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations, culminating in Landau's general theory of critical phenomena. Nowadays, it is understood that the common ground for all these phenomena lies in the presence of strong fluctuations of infinitely many coupled variables. This was made explicit first through the exact solution of the two-dimensional Ising model by Onsager. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical point, 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 emphasized today. This can be briefly summarized by saying that at a critical point a system is scale invariant. In addition, conformal invaTiance permits also a non-uniform, local rescal ing, provided only that angles remain unchanged.

Introduction to Conformal Invariance and Its Applications to Critical Phenomena
Introduction to Conformal Invariance and Its Applications to Critical Phenomena

Author: Philippe Christe

Publisher: Springer Science & Business Media

Published: 2008-09-11

Total Pages: 260

ISBN-13: 3540475753

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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.

Statistical Physics of Fields
Statistical Physics of Fields

Author: Mehran Kardar

Publisher: Cambridge University Press

Published: 2007-06-07

Total Pages: 376

ISBN-13: 1139855883

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While many scientists are familiar with fractals, fewer are familiar with scale-invariance and universality which underlie the ubiquity of their shapes. These properties may emerge from the collective behaviour of simple fundamental constituents, and are studied using statistical field theories. Initial chapters connect the particulate perspective developed in the companion volume, to the coarse grained statistical fields studied here. Based on lectures taught by Professor Kardar at MIT, this textbook demonstrates how such theories are formulated and studied. Perturbation theory, exact solutions, renormalization groups, and other tools are employed to demonstrate the emergence of scale invariance and universality, and the non-equilibrium dynamics of interfaces and directed paths in random media are discussed. Ideal for advanced graduate courses in statistical physics, it contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set available to lecturers at www.cambridge.org/9780521873413.