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 resul ts, 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 superco nducting film near H-cl we provide detailed scaling results for the statist ics of the magnetic flux density, susceptibility, heat capacity, and their cross correlations, which can be tested in a recently used experimental set up [Bolle er al., Nature (London) 399, 43 (1999)].