Parafermionic observables and their applications to planar statistical physics models

✍ Scribed by Hugo Duminil-Copin

• Publisher: SOCIEDADE BRASILEIRA DE MATEMATICA
• Year: 2013
• Tongue: English
• Leaves: 371
• Series: ENSAIOS MATEMATICOS 25
• Category: Library

✦ Synopsis

This volume is based on the PhD thesis of the author.
Through the examples of the self-avoiding walk, the random-cluster model,
the Ising model and others, the book explores in details two important
techniques:
1.Discrete holomorphicity and parafermionic observables, which have
been used in the past few years to study planar models of statistical
physics (in particular their conformal invariance), such as
random-cluster models and loop O(n)-models.
2. The Russo-Seymour-Welsh theory for percolation-type models with
dependence. This technique was initially available for Bernoulli
percolation only. Recently, it has been extended to models with
dependence, thus opening the way to a deeper study of their critical
regime.