The percolation phase transition and statistical multifragmentation in finite systems

The cumulant ratios up to fourth order of the $Z$ distributions of the largest fragment in spectator fragmentation following $^{107,124}$Sn+Sn and $^{124}$La+Sn collisions at 600 MeV/nucleon have been investigated. They are found to exhibit the signatures of a second-order phase transition established with cubic bond percolation and previously observed in the ALADIN experimental data for fragmentation of $^{197}$Au projectiles at similar energies. The deduced pseudocritical points are found to be only weakly dependent on the $A/Z$ ratio of the fragmenting spectator source. The same holds for the corresponding chemical freeze-out temperatures of close to 6 MeV. The experimental cumulant distributions are quantitatively reproduced with the Statistical Multifragmentation Model and parameters used to describe the experimental fragment multiplicities, isotope distributions and their correlations with impact-parameter related observables in these reactions. The characteristic coincidence of the zero transition of the skewness with the minimum of the kurtosis excess appears to be a generic property of statistical models and is found to coincide with the maximum of the heat capacity in the canonical thermodynamic fragmentation model.