Numerical Methods in the Study of Critical Phenomena


Book Description

This volume contains most of the lectures presented at the meeting held in Carry-le nd Rouet from the 2 to the 4th June 1980 and entitled "Numerical Methods in the Study of Critical Phenomena". Scientific subjects are becoming increasingly differentiated, and the number of journals and meetings devoted to them is continually increasing. Thus it has become very difficult for the non-specialist to approach subjects with which he is not familiar. Hence the purpose of our meeting was to bring together scientists from different disciplines to study a common subject and to stimulate discussion' between participants. We hope this goal was reached. The lectures are grouped in five chapters and, inside the first and the second chapter, under two headings. In each group they are classified in alphabetical order by author. We are pleased to publish these Proceedings in a series whose multidisciplinary character has been emphasized from the beginning. We are indebted to all who provided us with their help, particularly to Mrs. A. Litman of the Centre International de Rencontres Mathematiques at Luminy (C.I.R.M.) whose kindness and efficiency are well known; from the practical point of view, the meetings were organized within the scientific framework of the G.I.S. No.19 (C.N.R.S.), with the participation of the University of Grenoble.







Elements of Phase Transitions and Critical Phenomena


Book Description

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.




Stochastic Numerical Methods


Book Description

Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability Concepts Monte Carlo Integration Generation of Uniform and Non-uniform Random Numbers: Non-correlated Values Dynamical Methods Applications to Statistical Mechanics Introduction to Stochastic Processes Numerical Simulation of Ordinary and Partial Stochastic Differential Equations Introduction to Master Equations Numerical Simulations of Master Equations Hybrid Monte Carlo Generation of n-Dimensional Correlated Gaussian Variables Collective Algorithms for Spin Systems Histogram Extrapolation Multicanonical Simulations







Discrete Iterations


Book Description

a c 9 h In presenting this monograph, I would like to indicate both its orientation as well as my personal reasons for being interested in discrete iterations (that is, iterations on a generally very large,jinite set). While working in numerical analysis I have been interested in two main aspects: - the algorithmic aspect: an iterative algorithm is a mathematical entity which behaves in a dynamic fashion. Even if it is started far from a solution, it will often tend to get closer and closer. - the mathematical aspect: this consists of a coherent and rigorous analy sis of convergence, with the aid of mathematical tools (these tools are mainly the use of norms for convergence proofs, the use of matrix algebra and so on). One may for example refer to the algorithmic and mathematical aspects of Newton's method in JRn as well as to the QR algorithm for eigenvalues of matrices. These two algorithms seem to me to be the most fascinating algorithms in numerical analysis, since both show a remarkable practical efficiency even though there exist relatively few global convergence results for them.







Critical Dynamics


Book Description

A comprehensive and unified introduction to describing and understanding complex interacting systems.







Phase Transitions and Critical Phenomena


Book Description

The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. It has moved into a central place in condensed matter studies.Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations.The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.