This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.

This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.

This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

"This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.

Volume IAHandbook of Crystal Growth, 2nd Edition (Fundamentals: Thermodynamics and Kinetics) Volume IA addresses the present status of crystal growth science, and provides scientific tools for the following volumes: Volume II (Bulk Crystal Growth) and III (Thin Film Growth and Epitaxy). Volume IA highlights thermodynamics and kinetics. After historical introduction of the crystal growth, phase equilibria, defect thermodynamics, stoichiometry, and shape of crystal and structure of melt are described. Then, the most fundamental and basic aspects of crystal growth are presented, along with the theories of nucleation and growth kinetics. In addition, the simulations of crystal growth by Monte Carlo, ab initio-based approach and colloidal assembly are thoroughly investigated. Volume IBHandbook of Crystal Growth, 2nd Edition (Fundamentals: Transport and Stability) Volume IB discusses pattern formation, a typical problem in crystal growth. In addition, an introduction to morphological stability is given and the phase-field model is explained with comparison to experiments. The field of nanocrystal growth is rapidly expanding and here the growth from vapor is presented as an example. For the advancement of life science, the crystal growth of protein and other biological molecules is indispensable and biological crystallization in nature gives many hints for their crystal growth. Another subject discussed is pharmaceutical crystal growth. To understand the crystal growth, in situ observation is extremely powerful. The observation techniques are demonstrated. Volume IA - Explores phase equilibria, defect thermodynamics of Si, stoichiometry of oxides and atomistic structure of melt and alloys - Explains basic ideas to understand crystal growth, equilibrium shape of crystal, rough-smooth transition of step and surface, nucleation and growth mechanisms - Focuses on simulation of crystal growth by classical Monte Carlo, ab-initio based quantum mechanical approach, kinetic Monte Carlo and phase field model. Controlled colloidal assembly is presented as an experimental model for crystal growth. Volume IIB - Describes morphological stability theory and phase-field model and comparison to experiments of dendritic growth - Presents nanocrystal growth in vapor as well as protein crystal growth and biological crystallization - Interprets mass production of pharmaceutical crystals to be understood as ordinary crystal growth and explains crystallization of chiral molecules - Demonstrates in situ observation of crystal growth in vapor, solution and melt on the ground and in space