Synopses & Reviews
Conformally invariance has proven spectacularly useful for the understanding of two-dimensional phase transitions of classical systems at equilibrium. This volume presents an introduction to non-local observables such as loops and interfaces. It is explained how they arise from specific physical contexts and how to use conformal invariance to determine their properties. Stochastic Loewner Evolution represents an important conceptual advance, whose consequences provoked considerable interest by physicists and mathematicians alike. In this book, after an introductory chapter on the elements of conformal invariance, both the conceptual foundations of Stochastic Loewner Evolution as well as extensive numerical tests will be described. This is followed by applications to geometric phase transitions such as percolation or polymer systems, with particular attention to surface effects. The informal style of the book makes its contents accessible to graduate students and non-specialist readers from other fields.
Synopsis
Offering newcomers an introduction to the field, and seasoned researchers a wealth of current applications, this edited collection is a testament to the spectacular success and value of conformal invariance and the Stochastic Loewner Evolution of its method.
Synopsis
Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE's conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE's use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.
Table of Contents
A short Introduction to Conformal Invariance.- A Short Introduction to Critical Interfaces in 2D.- Numerical Tests of Schramm-Loewner Evolution in Random Lattice Spin Models.- Loop Models and Boundary CFT.- References.- Index.