The Renormalization Group For Disordered Systems
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The Renormalization Group For Disordered Systems
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Author : Michele Castellana
language : en
Publisher: Sapienza Università Editrice
Release Date : 2014-12-01
The Renormalization Group For Disordered Systems written by Michele Castellana and has been published by Sapienza Università Editrice this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-01 with Art categories.
Capire la natura del vetro è una delle questioni aperte più profonde nella fisica teorica della materia condensata. Oltre a essere un problema matematicamente molto complesso, comprendere la natura della fase vetrosa richiede intuizioni fisiche completamente nuove, che vanno al di là dei concetti usati nella fisica dei sistemi omogenei. Negli ultimi decenni si sono fatti progressi notevoli nello studio di modelli di campo medio per vetri di spin e vetri strutturali e la soluzione di questi modelli ha svelato una struttura della fase di bassa temperatura estremamente complessa. Tuttavia, non è ancora chiaro se le caratteristiche fisiche che emergono da queste soluzioni di campo medio descrivano anche i sistemi che esistono in natura, i quali sono rappresentati da modelli che vanno al di là del campo medio, detti anche modelli ‘non-mean-field’. Sfortunatamente, la soluzione di questi modelli non-mean-field si è dimostrata estremamente difficile, sia dal punto di vista analitico sia da quello numerico. Questo libro tratta di modelli non-mean-field di vetri di spin e vetri strutturali costruiti su reticolo gerarchico: si tratta dei modelli non-mean-field più semplici per i quali è possibile implementare in modo naturale una trasformazione di gruppo di rinormalizzazione. Questi metodi di gruppo di rinormalizzazione sono estremamente efficaci nell’aiutarci a comprendere la fisica di questi modelli di vetri. Attraverso essi, infatti, si mostra per la prima volta l’esistenza di una transizione di fase in un modello gerarchico non-mean-field di un vetro strutturale. Inoltre viene presentato un nuovo metodo di gruppo di rinormalizzazione per i vetri di spin, che si applica ad un modello di vetro di spin non-mean-field costruito su reticolo gerarchico: il metodo mostra l’esistenza di una transizione di fase, facendo inoltre predizioni quantitative per quantità fisiche come la temperatura e gli esponenti critici. The nature of glass is one of the deepest unsolved problems in condensed-matter theory. Besides being a mathematical challenge, a complete understanding of the nature of the glassy phase calls for completely new physical insights that go beyond the physics of homogeneous systems. A remarkable progress has been made in the last decades to understand mean-field models of spin and structural glasses, and the solution of these models unraveled a strikingly complex structure of the low-temperature phase. One of the biggest unsolved questions is whether the features of these mean-field solutions apply also to systems existing in Nature, which are represented by non-mean-field models. Unfortunately, the solution of non-mean-field glass models has proved extremely hard, both from the analytical and numerical point of view. The book focuses study on the non-mean-field models of spin and structural glasses built on a hierarchical lattice. These are the simplest non-mean-field glass models for which a renormalization-group (RG) transformation can be naturally implemented. Such RG methods have proved extremely powerful in tackling the complexity of these systems. By using the RG method, we show for the first time the existence of a phase transition for a non-mean-field hierarchical model of a structural glass. In addition, we propose a novel RG method for spin glasses, and we apply it to a non-mean-field hierarchical model of a spin glass. The method shows the existence of a phase transition and makes quantitative predictions for physical quantities, such as the critical temperature and the critical exponents.
Renormalization Group Analysis Of Nonequilibrium Phase Transitions In Driven Disordered Systems
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Author : Taiki Haga
language : en
Publisher: Springer
Release Date : 2019-01-24
Renormalization Group Analysis Of Nonequilibrium Phase Transitions In Driven Disordered Systems written by Taiki Haga and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-24 with Science categories.
This book investigates phase transitions and critical phenomena in disordered systems driven out of equilibrium. First, the author derives a dimensional reduction property that relates the long-distance physics of driven disordered systems to that of lower dimensional pure systems. By combining this property with a modern renormalization group technique, the critical behavior of random field spin models driven at a uniform velocity is subsequently investigated. The highlight of this book is that the driven random field XY model is shown to exhibit the Kosterlitz–Thouless transition in three dimensions. This is the first example of topological phase transitions in which the competition between quenched disorder and nonequilibrium driving plays a crucial role. The book also includes a pedagogical review of a renormalizaion group technique for disordered systems.
Introduction To The Replica Theory Of Disordered Statistical Systems
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Author : Viktor Dotsenko
language : en
Publisher: Cambridge University Press
Release Date : 2005-10-13
Introduction To The Replica Theory Of Disordered Statistical Systems written by Viktor Dotsenko and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-13 with Science categories.
This text describes the statistical mechanics of classical spin systems with quenched disorder. The first part covers the physics of spin-glass states using results obtained within the framework of the mean field theory of spin glasses. The second part is devoted to the theory of critical phenomena in the presence of weak quenched disorder. This includes a systematic derivation of the traditional renormalization group theory. In the third part Dotsenko describes other types of disordered systems, relating them to new results at the frontiers of modern research. The book is suitable for graduate students and researchers in the field of statistical mechanics of disordered systems.
Scaling And Disordered Systems
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Author : Fereydoon Family
language : en
Publisher: World Scientific
Release Date : 2002-05-30
Scaling And Disordered Systems written by Fereydoon Family and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-30 with Science categories.
Investigation of the fractal and scaling properties of disordered systems has recently become a focus of great interest in research. Disordered or amorphous materials, like glasses, polymers, gels, colloids, ceramic superconductors and random alloys or magnets, do not have a homogeneous microscopic structure. The microscopic environment varies randomly from site to site in the system and this randomness adds to the complexity and the richness of the properties of these materials. A particularly challenging aspect of random systems is their dynamical behavior. Relaxation in disordered systems generally follows an unusual time-dependent trajectory. Applications of scaling and fractal concepts in disordered systems have become a broad area of interdisciplinary research, involving studies of the physics, chemistry, mathematics, biology and engineering aspects of random systems. This book is intended for specialists as well as graduate and postdoctoral students working in condensed-matter or statistical physics. It provides state-of-the-art information on the latest developments in this important and timely topic. The book is divided into three parts: Part I deals with critical phenomena, Part II is devoted to discussion of slow dynamics and Part III involves the application of scaling concepts to random systems. The effects of disorder at the mesoscopic scale as well as the latest results on the dynamical properties of disordered systems are presented. In particular, recent developments in static and dynamic scaling theories and applications of fractal concepts to disordered systems are discussed. Contents:Fractal Dimensions and Corrections to Scaling for Critical Potts Clusters (A Aharony & J Asikainen)Scaling and Finite-Size Effects for the Critical Backbone (M Barthelem et al.)Percolation and Critical Phenomena of an Attractive Micellar System (F Mallamace et al.)Critical Fluctuations in the Breakdown of Disordered Systems (A Petri)Compaction of Granular Matter: A Short Review, and the Random Tetris Model (A Barrat & V Loreto)Why Conductivity Decreases with Pressure in Ion-Doped Polymers (J T Bendler et al.)Lack of Equilibration in a Model for Continuously Supercooled Liquids (F Corberi & A Coniglio)Vortex Matter out of Equilibrium (M Nicodemi)Scaling in the Atmosphere: On Global Laws of Persistence and Tests of Climate Models (A Bunde & S Havlin)Nonlinear Relaxation in Population Dynamics (M A Cirone et al.)Scaling in Cosmic Structures (L Pietronero et al.)Effect of Damage on the Roughness of Planar Cracks: The Case of the Random Fuse Model (S Zapperi et al.)and other papers Readership: Specialists as well as graduate and postdoctoral students in condensed-matter and statistical physics. Keywords:Disordered Systems;Critical Phenomena;Slow Dynamics;Scaling Concepts;Dynamical Properties;Fractal Concepts;Condensed Matter Physics;Statistical Physics;Fractals;Renormalization Group;Phase Transitions;Growth Phenomena;Scaling Phenomena;Collective Behavior;Materials Physics;Dynamical Phenomena
Topics In Disordered Systems
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Author : Charles M. Newman
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-09-23
Topics In Disordered Systems written by Charles M. Newman 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 1997-09-23 with Mathematics categories.
Disordered systems are statistical mechanics models in random environments. This lecture notes volume concerns the equilibrium properties of a few carefully chosen examples of disordered Ising models. The approach is that of probability theory and mathematical physics, but the subject matter is of interest also to condensed matter physicists, material scientists, applied mathematicians and theoretical computer scientists. (The two main types of systems considered are disordered ferromagnets and spin glasses. The emphasis is on questions concerning the number of ground states (at zero temperature) or the number of pure Gibbs states (at nonzero temperature). A recurring theme is that these questions are connected to interesting issues concerning percolation and related models of geometric/combinatorial probability. One question treated at length concerns the low temperature behavior of short-range spin glasses: whether and in what sense Parisi's analysis of the meanfield (or "infinite-range") model is relevant. Closely related is the more general conceptual issue of how to approach the thermodynamic (i.e., infinite volume) limit in systems which may have many complex competing states. This issue has been addressed in recent joint work by the author and Dan Stein and the book provides a mathematically coherent presentation of their approach.)
Random Walks Random Fields And Disordered Systems
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Author : Anton Bovier
language : en
Publisher: Springer
Release Date : 2015-09-21
Random Walks Random Fields And Disordered Systems written by Anton Bovier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-21 with Science categories.
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields.
Statistical Mechanics Of Disordered Systems
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Author : Anton Bovier
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-08
Statistical Mechanics Of Disordered Systems written by Anton Bovier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-08 with Mathematics categories.
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Scaling Phenomena In Disordered Systems
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Author : Roger Pynn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Scaling Phenomena In Disordered Systems written by Roger Pynn 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 2013-11-21 with Technology & Engineering categories.
This volume comprises the proceedings of a NATO Advanced Study Institute held in Geilo, Norway, between 8-19 April 1985. Although the principal support for the meeting was provided by the NATO Committee for Scientific Affairs, a number of additional sponsors also contributed, allowing the assembly of an unusually large number of internationally rec ognized speakers. Additional funds were received from: EXXON Research and Engineering Co. IBM (Europe) Institutt for energiteknikk (NorwaY) Institut Lauge-Langevin (France) The Norwegian Research Council for Science and Humanities NORDITA (Denmark) The Norwegian Foreign Office The U. S. Army Research, Development and Standardization Group (Europe) The U. S. National Science Foundation - The Norwegian Council for Science and Letters The organizing committee would like to take this opportunity to thank these contributors for their help in promoting a most exciting rewarding meeting. This Study Institute was the eighth of a series of meetings held in Geilo on subjects related to phase transitions. In contrast to previous meetings which were principally concerned with transitions in ordered systems, this school addressed the problems which arise when structural order is absent. The unifying feature among the subjects discussed at the school and the link to themes of earlier meetings was the concept of scaling.
Advances In Disordered Systems Random Processes And Some Applications
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Author : Pierluigi Contucci
language : en
Publisher: Cambridge University Press
Release Date : 2016-12-15
Advances In Disordered Systems Random Processes And Some Applications written by Pierluigi Contucci and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-15 with Science categories.
This book offers a unified perspective on the study of complex systems with contributions written by leading scientists from various disciplines, including mathematics, physics, computer science, biology, economics and social science. It is written for researchers from a broad range of scientific fields with an interest in recent developments in complex systems.
Disordered Systems
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Author : John Hertz
language : en
Publisher:
Release Date : 1985
Disordered Systems written by John Hertz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Inhomogeneous materials categories.