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Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.
Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.
The book provides an introduction to the physics which underlies phase transitions and to the theoretical techniques currently at our disposal for understanding them. It will be useful for advanced undergraduates, for post-graduate students undertaking research in related fields, and for established researchers in experimental physics, chemistry, and metallurgy as an exposition of current theoretical understanding. - ;Recent developments have led to a good understanding of universality; why phase transitions in systems as diverse as magnets, fluids, liquid crystals, and superconductors can be brought under the same theoretical umbrella and well described by simple models. This book describes the physics underlying universality and then lays out the theoretical approaches now available for studying phase transitions. Traditional techniques, mean-field theory, series expansions, and the transfer matrix, are described; the Monte Carlo method is covered, and two chapters are devoted to the renormalization group, which led to a break-through in the field. The book will be useful as a textbook for a course in `Phase Transitions', as an introduction for graduate students undertaking research in related fields, and as an overview for scientists in other disciplines who work with phase transitions but who are not aware of the current tools in the armoury of the theoretical physicist. - ;Introduction; Statistical mechanics and thermodynamics; Models; Mean-field theories; The transfer matrix; Series expansions; Monte Carlo simulations; The renormalization group; Implementations of the renormalization group. -
Describing the physical properties of quantum materials near critical points with long-range many-body quantum entanglement, this book introduces readers to the basic theory of quantum phases, their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions, assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances, such as the Fermi gas near unitarity, Dirac fermions, Fermi liquids and their phase transitions, quantum magnetism, and solvable models obtained from string theory. After introducing the basic theory, it moves on to a detailed description of the canonical quantum-critical phase diagram at non-zero temperatures. Finally, a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory.
This book treats the problem of phase transitions, emphasizing the generality and universality of the methods and models used. The course is basically concentrated on the problems of vacuum degeneration in macroscopic systems and a fundamental concept of quasiaverages by Bogolubov playing a special role in the theory of phase transitions and critical phenomena. An analysis of the connection between phase transition and spontaneous symmetry breaking in a macroscopic system allows a unique description of both first- and second-order phase transitions.The unique features of this book are:(i) a unique approach of describing first — as well as second-order phase transitions, based on the Bogolubov concept of quasi-averages.(ii) a detailed presentation of the material and at the same time a review of modern problems.(iii) a general character of developed ideas that could be applied to various particular systems of condensed matter physics, nuclear physics and high-energy physics.
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.
This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group.
Boltzmann's formula S = In[W(E)] defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay — for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and classify phase transitions in small systems. This is all possible within Boltzmann's original definition of the microcanonical ensemble.Starting from Boltzmann's formula, the book formulates the microcanonical thermodynamics entirely within the frame of mechanics. This way the thermodynamic limit is avoided and the formalism applies to small as well to other nonextensive systems like gravitational ones. Phase transitions of first order, continuous transitions, critical lines and multicritical points can be unambiguously defined by the curvature of the entropy S(E,N). Special attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum.The dependence of the liquid-gas transition of small atomic clusters under prescribed pressure is treated. Thus the analogue to the bulk transition can be studied. The book also describes the microcanonical statistics of the collapse of a self-gravitating system under large angular momentum.
This is a textbook which gradually introduces the student to the statistical mechanical study of the different phases of matter and to the phase transitions between them. Throughout, only simple models of both ordinary and soft matter are used but these are studied in full detail. The subject is developed in a pedagogical manner, starting from the basics, going from the simple ideal systems to the interacting systems, and ending with the more modern topics. The textbook provides the student with a complete overview, intentionally at an introductory level, of the theory of phase transitions. All equations and deductions are included.