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.

From the reviews:

"The book consists of 4 chapters, each giving an introduction to one of the following topics: conformal invariance, critical interfaces in 2D, numerical tests of Schramm-Loewner evolution in random spin models, and loop models and boundary CFT. ? All of the contributions are nicely written, with numerous illustrations and graphics, and they whet one's appetite to learn more about this rich and beautiful field ? or serve as a guide for further study and exploration." (Roland M. Friedrich, Mathematical Reviews, March, 2014)