Fluctuations in a small hard-disk system: Implicit finite size effects

The influence of implicit finite size effects on the fluctuation in the number of particles in a subvolume is studied for a small system of hard disks with a fixed number of particles. The implicit (or anomalous) finite size effects—that arise from the use of periodic boundary conditions—are taken into account by including the periodicity of the total system into a model pair correlation function. Two pair correlation functions are considered; the accurate Percus–Yevick result and an approximation proposed by Baus and Colot that yields an excellent isothermal compressibility. Although very good agreement with canonical ensemble Monte Carlo results is obtained in both cases, it appears that the theoretical expression obtained for the fluctuation in the number of particles is rather sensitive to the thermodynamic and structural information conveyed by the pair correlation function.