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Theory of Phase Transitions

2014-05-20 Science
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Release : 2014-05-20
Genre : Science
Kind : eBook
Book Rating : 497/5 ( reviews)

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Book Synopsis Theory of Phase Transitions by : Ya. G. Sinai

Download or read book Theory of Phase Transitions written by Ya. G. Sinai. This book was released on 2014-05-20. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Phase Transitions: Rigorous Results is inspired by lectures on mathematical problems of statistical physics presented in the Mathematical Institute of the Hungarian Academy of Sciences, Budapest. The aim of the book is to expound a series of rigorous results about the theory of phase transitions. The book consists of four chapters, wherein the first chapter discusses the Hamiltonian, its symmetry group, and the limit Gibbs distributions corresponding to a given Hamiltonian. The second chapter studies the phase diagrams of lattice models that are considered at low temperatures. The notions of a ground state of a Hamiltonian and the stability of the set of the ground states of a Hamiltonian are also introduced. Chapter 3 presents the basic theorems about lattice models with continuous symmetry, and Chapter 4 focuses on the second-order phase transitions and on the theory of scaling probability distributions, connected to these phase transitions. Specialists in statistical physics and other related fields will greatly benefit from this publication.

Landau Theory Of Phase Transitions, The: Application To Structural, Incommensurate, Magnetic And Liquid Crystal Systems

1987-08-01 Science
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Release : 1987-08-01
Genre : Science
Kind : eBook
Book Rating : 949/5 ( reviews)

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Book Synopsis Landau Theory Of Phase Transitions, The: Application To Structural, Incommensurate, Magnetic And Liquid Crystal Systems by : Pierre Toledano

Download or read book Landau Theory Of Phase Transitions, The: Application To Structural, Incommensurate, Magnetic And Liquid Crystal Systems written by Pierre Toledano. This book was released on 1987-08-01. Available in PDF, EPUB and Kindle. Book excerpt: The contents of this book stems from three different objectives. First, it is an introduction to the basic principles and techniques of Landau's theory, which is intended for teaching purposes. A second purpose of the book provides the practical methods for applying Landau's theory to complex systems. The last objective of the book is to incorporate the developments which have arisen in the last fifteen years from the extensive application of the theory to a variety of physical systems.

Phase Transitions

2011-08-14 Mathematics
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Release : 2011-08-14
Genre : Mathematics
Kind : eBook
Book Rating : 753/5 ( reviews)

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Book Synopsis Phase Transitions by : Ricard V. Solé

Download or read book Phase Transitions written by Ricard V. Solé. This book was released on 2011-08-14. Available in PDF, EPUB and Kindle. Book excerpt: Phase transitions--changes between different states of organization in a complex system--have long helped to explain physics concepts, such as why water freezes into a solid or boils to become a gas. How might phase transitions shed light on important problems in biological and ecological complex systems? Exploring the origins and implications of sudden changes in nature and society, Phase Transitions examines different dynamical behaviors in a broad range of complex systems. Using a compelling set of examples, from gene networks and ant colonies to human language and the degradation of diverse ecosystems, the book illustrates the power of simple models to reveal how phase transitions occur. Introductory chapters provide the critical concepts and the simplest mathematical techniques required to study phase transitions. In a series of example-driven chapters, Ricard Solé shows how such concepts and techniques can be applied to the analysis and prediction of complex system behavior, including the origins of life, viral replication, epidemics, language evolution, and the emergence and breakdown of societies. Written at an undergraduate mathematical level, this book provides the essential theoretical tools and foundations required to develop basic models to explain collective phase transitions for a wide variety of ecosystems.

Evolution of Phase Transitions

2006-05-08 Science
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Release : 2006-05-08
Genre : Science
Kind : eBook
Book Rating : 243/5 ( reviews)

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Book Synopsis Evolution of Phase Transitions by : Rohan Abeyaratne

Download or read book Evolution of Phase Transitions written by Rohan Abeyaratne. This book was released on 2006-05-08. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 work began with the author's exploration of the applicability of the finite deformation theory of elasticity when various standard assumptions such as convexity of various energies or ellipticity of the field equations of equilibrium are relinquished. The finite deformation theory of elasticity turns out to be a natural vehicle for the study of phase transitions in solids where thermal effects can be neglected. This text will be of interest to those interested in the development and application of continuum-mechanical models that describe the macroscopic response of materials capable of undergoing stress- or temperature-induced transitions between two solid phases. The focus is on the evolution of phase transitions which may be either dynamic or quasi-static, controlled by a kinetic relation which in the framework of classical thermomechanics represents information that is supplementary to the usual balance principles and constitutive laws of conventional theory.

Elements of Phase Transitions and Critical Phenomena

2011 Science
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Release : 2011
Genre : Science
Kind : eBook
Book Rating : 226/5 ( reviews)

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Book Synopsis Elements of Phase Transitions and Critical Phenomena by : Hidetoshi Nishimori

Download or read book Elements of Phase Transitions and Critical Phenomena written by Hidetoshi Nishimori. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.

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