Conformal invariance of lattice models
  These lecture notes provide a (almost) self-contained account on conformal invariance of the planar critical Ising and FK-Ising models. They present the theory of discrete holomorphic functions and its applications to planar statistical physics (more precisely to the convergence of fermionic observables). Convergence to SLE is discussed briefly. Many open questions are included. 
Hugo Duminil-Copin and Stanislav Smirnov
math.PR math-ph math.CO math.MP