ar X iv : n uc l - ex / 9 60 70 15 v 1 2 4 Ju l 1 99 6 DO PHASE TRANSITIONS SURVIVE BINOMIAL REDUCIBILITY AND THERMAL SCALING ?

First order phase transitions are described in terms of the microcanonical and canonical ensemble, with special attention to finite size effects. Difficulties in interpreting a " caloric curve " are discussed. A robust parameter indicating phase coexistence (univariance) or single phase (bivariance) is extracted for charge distributions. 1 Phase transitions, phase coexistence, and charge distributions Since the early studies of complex fragment emission at intermediate energies , a " liquid vapor phase transition " had been claimed as an explanation for the observed power law dependence of the fragment charge distribution. The basis for such claims was the Fisher droplet theory 1 which was advanced to explain/predict the clusterization of monomers in vapor. According to this theory, the probability of a cluster of size m is given by: P (m) ∝ e −(µ L −µ V)m kT m −τ e −csm 2/3 kT (1) where µ L , µ V are the liquid and vapor chemical potentials, τ is the Fisher critical exponent, c s the surface energy coefficient for the liquid. For µ V > µ L the liquid phase is stable and large clusters are found. For µ V < µ L the vapor is stable and small clusters are present. At the critical temperature the liquid-vapor distinction ends, µ L = µ V and the surface energy coefficient vanishes. The cluster size distribution assumes a characteristic power law dependence. A recent analysis of very detailed experiments has claimed not only the demonstration of a near critical regime, but also the determination of other critical coefficients 2 besides τ. Another recent announcement claiming the discovery of a first order phase transition associated with multifragmentation 3 has created a vast resonance. Because of the greater simplicity inherent to this subject and because of its relevance to some of our studies, we discuss it here in some detail. This study claims to have determined the " caloric curve " (sic) of a nucleus, namely the dependence of nuclear temperature on excitation energy. The temperature is determined from isotopic ratios (e.g.