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
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