Critical fluctuations in models with van der Waals interactions

Particle number fluctuations are considered within the van der Waals (VDW) equation, which contains both attractive (mean-field) and repulsive (eigenvolume) interactions. The VDW equation is used to calculate the scaled variance of particle number fluctuations in generic Boltzmann VDW system and in nuclear matter. The strongly intensive measures $\Delta[E^*,N]$ and $\Sigma[E^*,N]$ of the particle number and excitation energy fluctuations are also considered, and, similarly, show singular behavior near the critical point. The $\Delta[E^*,N]$ measure is shown to attain both positive and negative values in the vicinity of critical point. Based on universality argument, similar behavior is expected to occur in the vicinity of the QCD critical point.