The 2D Ising model near criticality: a FK percolation analysis
  We study the 2d-Ising model defined on finite boxes at temperatures that are below but very close from the critical point. When the temperature approaches the critical point and the size of the box grows fast enough, we establish large deviations estimates on FK-percolation events that concern the phenomenon of phase coexistence. 
Raphael Cerf and Reda Messikh