The course deals with various arguments related to the theory of the spin systems in statistical mechanics.
The course is based on various books and papers.
You can download here a Gallavotti's review on Ising model.
The basic reference for the theory of Markov chains is the book "Finite Markov chains and algorithmic applications" by Olle Haggstrom.
Here's an introductory paper on cutoff for Markov chains.
The results on cliques for Erdos random graphs can be found in the book "Random graphs" by Bela Bollobas.
About cluster expansion you can see the book under construction by Aldo Procacci.
This is the basic reference on the applications of cluster expansion to the theory of percolation .