Supermathematics And Its Applications In Statistical Physics

Author : Franz Wegner
Publisher : Springer
Page : 374 pages
File Size : 44,9 Mb
Release : 2016-03-25
Category : Science
ISBN : 9783662491706

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Supermathematics and its Applications in Statistical Physics by Franz Wegner Pdf

This text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical systems, as well as related topics in statistical physics. Based on many courses and seminars held by the author, one of the pioneers in this field, the reader is given a systematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables is presented in part I. The mathematics of these variables is applied to a random matrix model, path integrals for fermions, dimer models and the Ising model in two dimensions. Supermathematics - the use of commuting and anticommuting variables on an equal footing - is the subject of part II. The properties of supervectors and supermatrices, which contain both commuting and Grassmann components, are treated in great detail, including the derivation of integral theorems. In part III, supersymmetric physical models are considered. While supersymmetry was first introduced in elementary particle physics as exact symmetry between bosons and fermions, the formal introduction of anticommuting spacetime components, can be extended to problems of statistical physics, and, since it connects states with equal energies, has also found its way into quantum mechanics. Several models are considered in the applications, after which the representation of the random matrix model by the nonlinear sigma-model, the determination of the density of states and the level correlation are derived. Eventually, the mobility edge behavior is discussed and a short account of the ten symmetry classes of disorder, two-dimensional disordered models, and superbosonization is given.

Author : Hung T Diep
Publisher : World Scientific Publishing Company
Page : 648 pages
File Size : 40,9 Mb
Release : 2015-06-29
Category : Science
ISBN : 9789814696272

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Statistical Physics by Hung T Diep Pdf

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.

Author : Edouard Brézin,Shinobu Hikami
Publisher : Springer
Page : 138 pages
File Size : 54,5 Mb
Release : 2017-01-11
Category : Science
ISBN : 9789811033162

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Random Matrix Theory with an External Source by Edouard Brézin,Shinobu Hikami Pdf

This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.

Author : Norbert Euler,Da-jun Zhang
Publisher : CRC Press
Page : 367 pages
File Size : 41,9 Mb
Release : 2021-09-07
Category : Mathematics
ISBN : 9781000423303

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Nonlinear Systems and Their Remarkable Mathematical Structures by Norbert Euler,Da-jun Zhang Pdf

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained

Author : Slava Rychkov
Publisher : Springer Nature
Page : 71 pages
File Size : 54,8 Mb
Release : 2023-10-09
Category : Science
ISBN : 9783031420009

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Lectures on the Random Field Ising Model by Slava Rychkov Pdf

This book is about the Random Field Ising Model (RFIM) – a paradigmatic spin model featuring a frozen disordering field. The focus is on the second-order phase transition between the paramagnetic and ferromagnetic phases, and the associated critical exponents. The book starts by summarizing the current knowledge about the RFIM from experiments, numerical simulations and rigorous mathematical results. It then reviews the classic theoretical works from the 1970’s which suggested a property of dimensional reduction – that the RFIM critical exponents should be the same as for the ordinary, non-disordered, Ising model of lower dimensionality, and related this an emergent Parisi-Sourlas supersymmetry. As is now known, these remarkable properties only hold when the spatial dimensionality of the model is larger than a critical dimension. The book presents a method to estimate the critical dimension, using standard tools such as the replica trick and perturbative renormalization group, whose result is in agreement with the numerical simulations. Some more elementary steps in the derivations are left as exercises for the readers. This book is of interest to researchers, PhD students and advanced master students specializing in statistical field theory.

Author : George H. Weiss
Publisher : SIAM
Page : 267 pages
File Size : 46,5 Mb
Release : 1994-01-01
Category : Science
ISBN : 1611971551

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Contemporary Problems in Statistical Physics by George H. Weiss Pdf

This collection of independent articles describes some mathematical problems recently developed in statistical physics and theoretical chemistry. The book introduces and reviews current research on such topics as nonlinear systems and colored noise, stochastic resonance, percolation, the trapping problem in the theory of random walks, and diffusive models for chemical kinetics. Some of these topics have never before been presented in expository book form. Applied mathematicians will be introduced to some contemporary problems in statistical physics. In addition, a number of unsolved problems currently attracting intensive research efforts are described, and some of the techniques used in this research are outlined, along with principal results and outstanding questions. A wide spectrum of mathematical techniques is covered, but the main emphasis is on introducing the mathematician to different research areas with open and interesting problems. This is an ideal starting point for the mathematician with an elementary acquaintance with the methodology of statistical physics. The material is meant to be introductory and terms are carefully defined. Many topics that require further study are introduced, providing new research ideas for the applied mathematician or thesis problems for the graduate student.

Author : Honerkamp
Publisher : Unknown
Page : 532 pages
File Size : 46,5 Mb
Release : 2004-01-01
Category : Electronic
ISBN : 818128125X

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Statistical Physics, 2E by Honerkamp Pdf

Author : Giuseppe Mussardo
Publisher : Oxford University Press
Page : 1154 pages
File Size : 51,6 Mb
Release : 2020-03-26
Category : Science
ISBN : 9780191092176

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Statistical Field Theory by Giuseppe Mussardo Pdf

Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides a thorough introduction to the fascinating world of phase transitions and frontier topics of exactly solved models in statistical mechanics and quantum field theory, such as renormalization groups, conformal models, quantum integrable systems, duality, elastic S-matrices, thermodynamic Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics distinguished for their elegance and beauty, including infinite dimensional algebras, conformal mappings, integral equations and modular functions. Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail while providing overall coherent understanding of physical phenomena. Mathematical background is made available in supplements at the end of each chapter, when appropriate. The chapters include problems of different levels of difficulty. Advanced undergraduate and graduate students will find this book a rich and challenging source for improving their skills and for attaining a comprehensive understanding of the many facets of the subject.

Author : Robert Adolʹfovich Minlos
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 55,5 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821813379

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Introduction to Mathematical Statistical Physics by Robert Adolʹfovich Minlos Pdf

This book presents a mathematically rigorous approach to the main ideas and phenomena of statistical physics. The introduction addresses the physical motivation, focusing on the basic concept of modern statistical physics, that is the notion of Gibbsian random fields. Properties of Gibbsian fields are analysed in two ranges of physical parameters: "regular" (corresponding to high-temperature and low-density regimes) where no phase transition is exhibited, and "singular" (low temperature regimes) where such transitions occur. Next, a detailed approach to the analysis of the phenomena of phase transitions of the first kind, the Pirogov-Sinai theory, is presented. The author discusses this theory in a general way and illustrates it with the example of a lattice gas with three types of particles. The conclusion gives a brief review of recent developments arising from this theory. The volume is written for the beginner, yet advanced students will benefit from it as well. The book will serve nicely as a supplementary textbook for course study. The prerequisites are an elementary knowledge of mechanics, probability theory and functional analysis.

Author : FRITZ,JAFFE,SZASZ
Publisher : Springer Science & Business Media
Page : 489 pages
File Size : 54,9 Mb
Release : 2013-11-22
Category : Science
ISBN : 9781489966537

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Statistical Physics and Dynamical Systems by FRITZ,JAFFE,SZASZ Pdf

Author : Roger Balian
Publisher : Unknown
Page : 128 pages
File Size : 50,9 Mb
Release : 2007
Category : Electronic
ISBN : OCLC:1075457534

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From Microphysics to Macrophysics by Roger Balian Pdf

Author : Angelo Vulpiani,Fabio Cecconi,Massimo Cencini,Andrea Puglisi,Davide Vergni
Publisher : Springer
Page : 323 pages
File Size : 50,6 Mb
Release : 2014-05-16
Category : Science
ISBN : 9783642542510

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Large Deviations in Physics by Angelo Vulpiani,Fabio Cecconi,Massimo Cencini,Andrea Puglisi,Davide Vergni Pdf

This book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.

Author : Valerio Lucarini,Davide Faranda,Ana Cristina Gomes Monteiro Moreira de Freitas,Jorge Miguel Milhazes de Freitas,Mark Holland,Tobias Kuna,Matthew Nicol,Mike Todd,Sandro Vaienti
Publisher : John Wiley & Sons
Page : 325 pages
File Size : 46,9 Mb
Release : 2016-04-25
Category : Mathematics
ISBN : 9781118632192

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Extremes and Recurrence in Dynamical Systems by Valerio Lucarini,Davide Faranda,Ana Cristina Gomes Monteiro Moreira de Freitas,Jorge Miguel Milhazes de Freitas,Mark Holland,Tobias Kuna,Matthew Nicol,Mike Todd,Sandro Vaienti Pdf

Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.

Author : Jean Ruiz,Salvador Miracle-sole,Valentin Zagrebnov
Publisher : World Scientific
Page : 554 pages
File Size : 52,5 Mb
Release : 1999-05-14
Category : Electronic
ISBN : 9789814543781

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Mathematical Results In Statistical Mechanics by Jean Ruiz,Salvador Miracle-sole,Valentin Zagrebnov Pdf

This invaluable book is a collection of lectures delivered at the Colloquium 'Mathematical Results in Statistical Mechanics' held in Marseilles, France, on July 27-31, 1998, as a satellite colloquium of the Paris conference STATPHYS 20. It covers a large part of the contemporary results in statistical mechanics, from the point of view of mathematical physics, by leading experts in this field. It includes as the main topics, phase transitions, interfaces, disordered systems, Gibbsian and non-Gibbsian states, as well as recent rigorous treatments in quantum statistical mechanics.

Author : Edouard Brezin,Spenta R Wadia
Publisher : World Scientific
Page : 1149 pages
File Size : 48,7 Mb
Release : 1993-08-31
Category : Science
ISBN : 9789814506632

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The Large N Expansion In Quantum Field Theory And Statistical Physics by Edouard Brezin,Spenta R Wadia Pdf

This book contains an edited comprehensive collection of reprints on the subject of the large N limit as applied to a wide spectrum of problems in quantum field theory and statistical mechanics. The topics include (1) Spin Systems; (2) Large N Limit of Gauge Theories; (3) Two-Dimensional QCD; (4) Exact Results on Planar Perturbation Series and the Nature of the 1/N Series; (5) Schwinger-Dyson Equations Approach; (6) QCD Phenomenological Lagrangians and the Large N Limit; (7) Other Approaches to Large N: Eguchi-Kawai Model, Collective Fields and Numerical Methods; (8) Matrix Models; (9) Two-Dimensional Gravity and String Theory.