Ising model

Ising Models are important for Machine Learning because they are well-studied physical counter-parts of binary valued undirected graphical models. Belief Propagation in such models is equivalent to iteration of the Bethe-Pieirls fixed point equations. Recently Michael Chertkov and Vladimir Chernyak formulated an expression that gave exact expression for the partition function in terms of a local BP solution (slides), and Gómez,Mooij,Kappen followed up by truncating the exact expression and applying it to diagnostic inference task (related slides, approach based on method by Montanari and Rizzo)slides)

While catching up on Ising models, here are a few Ising Model introductory materials I've scanned/scavenged

• Sang Hoon Lee: Introduction to Ising Model and Opinion Dynamics for non-physicists -- basic concept of the Ising model.
  
  
• Rasaiah: Statistical mechanics of strongly interacting systems, chapter from Encyclopedia of Chemical Physics and Physical Chemistry -- solution for 1d Ising model, with and without magnetic field.
  
  
• Dorogovtsev et al: Critical phenomena in complex networks -- Chapter 6 gives algorithms for Ising model, relates to graphical model formalism
  
  
• Salinas: Ising Model, chapter from "Introduction to Statistical Physics" -- Ising model on a lattice, mean field and BP approximation, Curie-Weiss model