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A Modern critical phenomena par Herbut, Igor. Publication : Cambridge : Cambridge University Press 2010 . pages cm. Date : 2010 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Complexity and criticality par Christensen, Kim. Publication : London Imperial College Press 2005 . 392 p. , This book provides a challenging and stimulating introduction to the contemporary topics of complexity and criticality, and explores their common basis. Criticality refers to the behaviour of extended systems at a phase transition where scale invariance prevails; the many constituent microscopic parts bringing about macroscopic phenomena that cannot be understood by considering a single part alone. The phenomenology of phase transitions is introduced by considering percolation, a simple model with a purely geometrical percolating phase transition, thus enabling the reader to become intuitively familiar with concepts such as scale invariance and renormalisation. The Ising model, meanwhile, is a simple model capturing the phase transition from a disordered to an ordered system as the temperature is lowered in zero external field. By emphasising analogies between percolation and the Ising model, the reader's intuition of phase transitions is developed so that the underlying theoretical formalism may be appreciated fully. These equilibrium systems undergo a phase transition only if an external agent finely tunes certain external parameters to particular values. Besides fractals and phase transitions, there are many examples in Nature of the emergence of such complex behaviour in slowly driven non-equilibrium systems: earthquakes in seismic systems, avalanches in granular media and rainfall in the atmosphere. A class of non-equilibrium systems, with no constraints in having to tune external parameters to obtain critical behaviour, is addressed in the framework of simple models, revealing that repeated application of simple rules might spontaneously give rise to emergent complex behaviour not encoded in the rules themselves. The common basis of complexity and criticality is identified and applied to a range of non-equilibrium systems. Finally, the reader is invited to speculate whether self-organisation in non-equilibrium systems might be a unifying concept for disparate fields such as statistical mechanics, geophysics and atmospheric physics. 23 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Equilibrium statistical physics par Plischke,, Michael. Publication : [S.l.] World Scientific Pub Co Inc 2006 . 640 p. , This third edition of one of the most important and best selling textbooks in statistical physics, is a graduate level text suitable for students in physics, chemistry, and materials science. Highlights of the book include a discussion of strongly interacting condensed matter systems with a thorough treatment of mean field and Landau theories of phase transitions. Discussions of the Potts model and the asymmetric exclusion process have been added. Along with traditional approaches to the subject such as the virial expansion and integral equations, newer theories such as perturbation theory and density functional theories are introduced. The modern theory of phase transitions occupies a central place in this book. A separate, largely rewritten, chapter is devoted to the renormalization group approach to critical phenomena, with detailed discussion of the basic concepts of this important technique and examples of both exact and approximate calculations given. The development of the basic tools is completed in an expanded chapter on computer simulations in which both Monte Carlo and molecular dynamics techniques are introduced. 23 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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How nature works the science of self-organized criticality par Bak, Per. Publication : New York Springer 1996 . xiii-212 p. , Self-organized criticality, the spontaneous development of systems to a critical state, is the first general theory of complex systems with a firm mathematical basis. This theory describes how many seemingly desperate aspects of the world, from stock market crashes to mass extinctions, avalanches to solar flares, all share a set of simple, easily described properties. "...a'must read'...Bak writes with such ease and lucidity, and his ideas are so intriguing...essential reading for those interested in complex systems...it will reward a sufficiently skeptical reader." -NATURE "...presents the theory (self-organized criticality) in a form easily absorbed by the non-mathematically inclined reader." -BOSTON MONO REVIEW "I picture Bak as a kind of scientific musketeer; flamboyant, touchy, full of swagger and ready to join every fray... His book is written with panache. The style is brisk, the content stimulating. I recommend it as a bracing experience." -NEW SCIENTIST. 23 cm. Date : 1996 Disponibilité : Exemplaires disponibles: La bibliothèque des sciences de l'ingénieur (1),

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Quantum field theory and critical phenomena par Zinn-Justin, Jean. Publication : [S.l.] Oxford University Press, USA 2002 . 1074 p. , The book is an introduction to quantum field theory and renormalization group. It shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of physics, which range from phase transitions in macroscopic systems to the theory of fundamental interactions. This advanced new edition is based on graduate courses and summer schools given by the author over a number of years. Although there are several good textbooks on QFT, this is the first to emphasize the common aspects of particle physics and the theory of critical phenomena in a unified framework. The book has been fully updated, with about 50% new material added. Three new chapters have been included: an introduction to non-relativistic quantum statistical physics; a chapter on critical phenomena in non-magnetic systems, polymers, liquid-vapour, and helium superfluid transitions; and a chapter on finite temperature relativistic quantum field theory. The book can be roughly divided into four parts: chapters 1-12 deal with general field theory, functional integrals, and functional methods. In chapters 13-21, renormalization properties of theories with symmetries are studied and specific applications to particle physics are emphasized. Chapters 23-37 are devoted to critical phenomena. Chapters 39-43 describe the role of instantons in quantum mechanics and field theory. 25 cm. Date : 2002 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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