Phase Transitions Cargèse 1980

ISBN-13: 9781461333494 / Angielski / Miękka / 2011 / 462 str.

J. Levy; Jean Zinn-Justin; Maurice Levy

Opis

The understanding of phase transitions has long been a fundamental problem of statistical mechanics. It has made spectac ular progress during the last few years, largely because of the ideas of K.G. Wilson, in applying to an apparently quite different domain the methods of the renormalization group, which had been developped in the framework of the quantum theory of fields. The ability of these theoretical methods to lead to very precise predictions has, n turn, stimulated in the last few years more refined experiments in different areas. We now have entered a period where the theoretical results yielded by the renormalization group approach are suffi ciently precise and can be compared with those of the traditional method of high temperature series expansion on lattices, and with the experimental data. Although very similar, the results coming from the renormalization group and high temperature analysis seemed to indicate systematic discrepancies between the continuous field theory and lattice models. It was therefore important to appreciate the reliability of the predictions coming from both theoretical schemes, and to compare them to the latest experimental results. We think that this Cargese Summer Institute has been very successful 1 in this respect. Indeed, leading experts in the field, both experimentalists and theoreticians, have gathered and presented detailed analysis of the present situation. In particular, B.G. Nickel has produced longer high temperature series which seem to indicate that the discrepancies between series and renormalization group results have been previously overestimated."

Spis treści

Static and Dynamic Critical Phenomena Near the Superfluid Transition in 4He.- Status of the Experimental Situation in Critical Binary Fluids.- Thermodynamic Anomalies Near the Liquid-Vapor Critical Point: A Review of Experiments.- Universality of Critical Phenomena in Classical Fluids.- An Analysis of the Continuous-Spin, Ising Model.- What is Series Extrapolation About?.- High Temperature Series, Universality and Scaling Corrections.- Bicriticality and Partial Differential Approximants.- High Temperature Series Analysis for the Three-Dimensional Ising Model: A Review of Some Recent Work.- Derivation of High Temperature Series Expansions: Ising Model.- Series Expansions for the Classical Vector Model.- The Problem of Confluent Singularities.- Differential Approximants and Confluent Singularities Analysis.- Critical Behaviour from the Field Theoretical Renormalization Group Techniques.- Calculation of Critical Exponents from Field Theory.- Theory of Polymers in Solution.- Monte-Carlo Renormalization Group.- Critical Behaviour in Interfaces.