Critical point multiplicities and multiplicity fluctuations in heavy ion collisions

An exactly solvable thermodynamic model of nuclear fragmentation exhibiting a phase transition is shown to lead to a simple connection between the critical point multiplicity 〈m〉c and the critical point exponent τ. This transition is characterized by large multiplicity fluctuations and the sudden appearance of very large clusters. The model agrees in many respects with the critical properties recently extracted experimentally by the EOS collaboration from the behavior of the reduced moments. Parallels of our model with percolation theory and Bose-Einstein condensation are discussed.