Distributions of the largest fragment size in multifragmentation: Traces of a phase transition

Abstract

Distributions of the largest fragment charge are studied using the ALADIN data on fragmentation of 197 Au projectiles at relativistic energies. The statistical measures skewness and kurtosis of higher-order fluctuations provide a robust indication of the transition point, linked to a phase transition in the thermodynamic limit. Extensive comparisons with predictions of a bond percolation model corroborate the high accuracy of this model in reproducing the distributions as well as the whole fragmentation pattern as represented by the measured charge correlations. In analogy to percolation, the pseudocritical and critical points are identified in the fragmentation data.Questions concerning the distinction between different models and between first-and second-order phase transitions are discussed.

The percolation phase transition and statistical multifragmentation in finite systems

“…and kurtosis excess of higher-order fluctuations of the largest fragment size provide a robust indication of the transition point, linked to a second-order phase transition in the continuous limit [1]. The characteristic signatures identified with bond percolation calculations were found to be present in the ALADIN fragmentation data reported by Schüttauf et al [2] for 197 Au projectiles at 600 to 1000 MeV/nucleon in collisions with several targets [3]. Comparisons made with calculations for estimated system sizes demonstrated the high accuracy of the percolation model in reproducing the distributions of the largest fragment charge (atomic number Z) as well as the whole fragmentation pattern as represented by various forms of charge correlations.…”

“…The coincidence of the zero transition of the skewness and the minimum of the kurtosis excess with a value near -1 is very precise and persists if the size of the system is varied. The maximum of the normalized variance K 2 is located at or very close to the critical bond-breaking parameter [1,3].…”

“…Comparisons made with calculations for estimated system sizes demonstrated the high accuracy of the percolation model in reproducing the distributions of the largest fragment charge (atomic number Z) as well as the whole fragmentation pattern as represented by various forms of charge correlations. In analogy to percolation, the critical and pseudocritical points were identified in the fragmentation data [3].…”

“…The largest fragment is expected to represent the liquid part of the system and thus to assume the role of the order parameter in a manifestation of the liquid-gas phase transition in finite systems, providing valuable insight into their phase behavior (for reports and reviews see, e.g., Refs. [3,15,16,17,18,19,20,21,22,23] and references given therein).…”

“…The high efficiency of close to 100% for the detection of projectile fragments is an important property of the setup [2]. Tests performed for the case of 197 Au fragmentation confirmed that possible minor inefficiencies have negligible effects on the studied cumulant ratios [3].…”