This book presents a short, fairly simple course on the basic theory of phase transitions and its modern applications. In physics, these applications include such modern developments as Bose-Einstein condensation of atoms, high temperature superconductivity, and vortices in superconductors, while in other fields they include small world phenomena and scale-free systems (such as stock markets and the Internet). The advantage of treating all these topics together lies in showing their connection with one another and with the general theory of phase transitions.
This book provides a comprehensive review of the theory of phase transitions and its modern applications, based on the five pillars of the modern theory of phase transitions: the Ising model, mean field, scaling, renormalization group and universality. This expanded second edition includes, along with a description of vortices and high temperature superconductivity, a discussion of phase transitions in chemical reactions and moving systems. The book covers the close connection between phase transitions and small world phenomena as well as scale-free systems such as the stock market and the Internet.
- A short but comprehensive description of the five pillars of the modern theory of phase transitions - A general survey of numerous modern applications of the theory of phase transitions, rather than treatment of a single topic in great detail, as in most textbooks - Suitable for incorporating in a graduate or advanced undergraduate course on statistical physics - Provides a good minimum basis for under-standing current research on the application of statistical mechanics to problems in different fields, such as science, economics and sociology
Attempts to understand various aspects of the empirical world often rely on modelling processes that involve a reconstruction of systems under investigation. Typically the reconstruction uses mathematical frameworks like gauge theory and renormalization group methods, but more recently simulations also have become an indispensable tool for investigation. This book is a philosophical examination of techniques and assumptions related to modelling and simulation with the goal of showing how these abstract descriptions can contribute to our understanding of the physical world. Particular issues include the role of fictional models in science, how mathematical formalisms can yield physical information, and how we should approach the use of inconsistent models for specific types of systems. It also addresses the role of simulation, specifically the conditions under which simulation can be seen as a technique for measurement, replacing more traditional experimental approaches. Inherent worries about the legitimacy of simulation "knowledge" are also addressed, including an analysis of verification and validation and the role of simulation data in the search for the Higgs boson. In light of the significant role played by simulation in the Large Hadron Collider experiments, it is argued that the traditional distinction between simulation and experiment is no longer applicable in some contexts of modern science. Consequently, a re-evaluation of the way and extent to which simulation delivers empirical knowledge is required. "This is a, lively, stimulating, and important book by one of the main scholars contributing to current topics and debates in our field. It will be a major resource for philosophers of science, their students, scientists interested in examining scientific practice, and the general scientifically literate public."-Bas van Fraassen, Distinguished Professor of Philosophy, San Francisco State University
This volume collects several in-depth articles giving lucid discussions on new developments in statistical and condensed matter physics. Many, though not all, contributors had been in touch with the late S-K Ma. Written by some of the world's experts and originators of new ideas in the field, this book is a must for all researchers in theoretical physics. Most of the articles should be accessible to diligent graduate students and experienced readers will gain from the wealth of materials contained herein.
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.
Phases of Matter and their Transitions An all-in-one, comprehensive take on matter and its phase properties In Phases of Matter and their Transitions, accomplished materials scientist Dr. Gijsbertus de With delivers an accessible textbook for advanced students in the molecular sciences. It offers a balanced and self-contained treatment of the thermodynamic and structural aspects of phases and the transitions between them, covering solids, liquids, gases, and their interfaces. The book lays the groundwork to describe particles and their interactions from the perspective of classical and quantum mechanics and compares phenomenological and statistical thermodynamics. It also examines materials with special properties, like glasses, liquid crystals, and ferroelectrics. The author has included an extensive appendix with a guide to the mathematics and theoretical models employed in this resource. Readers will also find: Thorough introductions to classical and quantum mechanics, intermolecular interactions, and continuum mechanics Comprehensive explorations of thermodynamics, gases, liquids, and solids Practical discussions of surfaces, including their general aspects for solids and liquids Fulsome treatments of discontinuous and continuous transitions, including discussions of irreversibility and the return to equilibrium Perfect for advanced students in chemistry and physics, Phases of Matter and their Transitions will also earn a place in the libraries of students of materials science.
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.
