We propose to describe correlations in classical and
quantum systems in terms of full counting statistics (FCS) of a suitably chosen
discrete observable. Thermodynamic phases may be characterized by analytical
properties of the extensive part of the FCS. We illustrate our construction
with three examples: the classical Ising chain, the spin-1/2 XY chain, and free
fermions in one dimension. In the last example, we conjecture an asymptotic expansion
for the FCS, which generalizes the Fisher-Hartwig conjecture for Toeplitz
determinants. This expansion also determines finite-size corrections to the
entanglement entropy.
