Thermodynamic Fingerprints of Disorder in Flux Line Lattices and other   Glassy Mesoscopic Systems
  We examine probability distributions for thermodynamic quantities in finite-sized random systems close to criticality. Guided by available exact results, a general ansatz is proposed for replicated free energies, which leads to scaling forms for cumulants of various macroscopic observables. For the specific example of a planar flux line lattice in a two dimensional superconducting film near H_c1, we provide detailed results for the statistics of the magnetic flux density, susceptibility, heat capacity, and their cross-correlations. 
Thorsten Emig and Mehran Kardar