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1. Universal scaling relations for logarithmic-correction exponents / R. Kenna -- 2. Phase behaviour and criticality in primitive models of ionic fluids / O.V. Patsahan and I.M. Mryglod -- 3. Monte Carlo simulations in statistical physics-from basic principles to advanced applications / W. Janke -- 4. Ising model on connected complex networks / K. Suchecki and J.A. Hołyst -- 5. Minority game: an "Ising model" of econophysics / F. Slanina
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.
In condensed matter physics, researchers study the physical properties of condensed phases of matter, theoretically or experimentally. The fundamentally appealing topic in this research area is how to classify phases of matter and identify phase transitions between them.Different from traditional theoretical or experimental approaches, which relies on either complicated mathematical formulation or equally complex experimental equipment, Monte Carlo based stochastic methods, which are often treated as "computer experiments", introduce a relatively "cheap" but effective approach to study phases and phase transitions. In this dissertation, we employ the classical Monte Carlo simulation, which utilizes the Metropolis algorithm to evolve system configurations, and also the determinant quantum Monte Carlo simulation to study phases and phase transitions of model Hamiltonians, such as the Hubbard model, and the periodic Anderson model (PAM). In the 21st century, data driven machine learning techniques have proven to be an another research "engine" for detecting phases and phase transitions. In this dissertation, I explore potential usages of unsupervised machine learning techniques in phase transition. Specifically, I leverage the principal component analysis (PCA) to extract internal structures, which are fully reflected in leading principal components, of Monte Carlo generated configurations, and then quantify obtained principal components to distinguish phases and phase transitions. This technique is applied to study model Hamiltonians, such as the Ising model, the XY model, the Hubbard model and the PAM. The exact organization of this dissertation is as follows: In chapter 1, I first introduce basic concepts of phase transitions and related model Hamiltonians. In chapter 2, I talk about a variety of methodologies utilized. In chapter 3, I present studies of phase transitions in a spin-fermion model. In chapter 4, I explore phase diagrams of the PAM coupled with an additional layer of metal. In chapter 5 and 6, I discuss how to apply machine learning techniques, especially PCA, to distinguish phases and detect phase transitions in classical and quantum model Hamiltonians. In chapter 7, I summarize previous chapters and discuss potential future directions.
This book deals with the phenomenological theory of first-order structural phase transitions, with a special emphasis on reconstructive transformations in which a group-subgroup relationship between the symmetries of the phases is absent. It starts with a unified presentation of the current approach to first-order phase transitions, using the more recent results of the Landau theory of phase transitions and of the theory of singularities. A general theory of reconstructive phase transitions is then formulated, in which the structures surrounding a transition are expressed in terms of density-waves, providing a natural definition of the transition order-parameters, and a description of the corresponding phase diagrams and relevant physical properties. The applicability of the theory is illustrated by a large number of concrete examples pertaining to the various classes of reconstructive transitions: allotropic transformations of the elements, displacive and order-disorder transformations in metals, alloys and related structures, crystal-quasicrystal transformations.
A classical metastable state possesses a local free energy minimum at infinite sizes, but not a global one. This concept is phase size independent. We have studied a number of experimental results and proposed a new concept that there exists a wide range of metastable states in polymers on different length scales where their metastability is critically determined by the phase size and dimensionality. Metastable states are also observed in phase transformations that are kinetically impeded on the pathway to thermodynamic equilibrium. This was illustrated in structural and morphological investigations of crystallization and mesophase transitions, liquid-liquid phase separation, vitrification and gel formation, as well as combinations of these transformation processes. The phase behaviours in polymers are thus dominated by interlinks of metastable states on different length scales. This concept successfully explains many experimental observations and provides a new way to connect different aspects of polymer physics. * Written by a leading scholar and industry expert* Presents new and cutting edge material encouraging innovation and future research* Connects hot topics and leading research in one concise volume
Studies of surfaces and interactions between dissimilar materials or phases are vital for modern technological applications. Computer simulation methods are indispensable in such studies and this book contains a substantial body of knowledge about simulation methods as well as the theoretical background for performing computer experiments and analyzing the data. The book is self-contained, covering a range of topics from classical statistical mechanics to a variety of simulation techniques, including molecular dynamics, Langevin dynamics and Monte Carlo methods. A number of physical systems are considered, including fluids, magnets, polymers, granular media, and driven diffusive systems. The computer simulation methods considered include both standard and accelerated versions. The simulation methods are clearly related to the fundamental principles of thermodynamics and statistical mechanics.
Continuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics. Developed over the last two decades, it is based on the mathematical theory of nonlinear thermoelasticity, in which a new viewpoint on material symmetry, motivated by molecular theories, plays a c
The Advanced Study Institute on Phase Transitions in Surface Films was held at the Ettore Majorana Centre for Scientific Cul ture in Erice, Sicily, during June 11 to June 25, 1979. This Institute was the second course of the International School of Low Temperature Physics which was established at the Centre in 1977, with the guidance and inspiration of T. Regge and A. Zichichi. The 1979 course selected a topic on one of the most rapidly advancing fields of condensed matter physics in the late 70's. The program of topics and speakers was developed with the advice of the Organizing Committee, composed of J. Friedel, N. D. Mermin, R. E. Peierls, T. Regge and J. Wheatley. These two weeks were memorable for the range and depth of the lectures and seminars, and the sustained high interest of the students and faculty through a damanding schedule of over 5 hours a day of formal sessions. A large fraction of the leading researchers in the field were there. It would have been impossible to gather such a large group five years earlier, for the field itself is hardly 10 years old. Although the foundations of the thermodynamics of surface films were laid down by Gibbs about 100 years ago, and experiments on oil/water monolayers were carried out by Pockels and Rayleigh at about the same time, the beginnings of the modern field were much more recent.