Critical percolation and lack of self-averaging in disordered models
  Lack of self-averaging originates in many disordered models from a fragmentation of the phase space where the sizes of the fragments remain sample-dependent in the thermodynamic limit. On the basis of new results in percolation theory, we give here an argument in favour of the conjecture that critical two dimensional percolation on the square lattice lacks of self-averaging. 
Andrea De Martino and Andrea Giansanti (Dip. Fisica, Univ. di Roma "La   Sapienza", Roma, Italy)