Abstract:
The resilience to averaging over an initial energy distribution of reducibility and thermal scaling observed in nuclear multifragmentation is studied. Poissonian reducibility and the associated thermal scaling of the mean are shown to be robust. Binomial reducibility and thermal scaling of the elementary probability are robust under a broad range of conditions. The experimental data do not show any indication of deviation due to averaging.

Abstract:
It is shown that the Fisher Droplet Model (FDM), percolation and nuclear multifragmentation share the common features of reducibility (stochasticity in multiplicity distributions) and thermal scaling (one-fragment production probabilities are Boltzmann factors). Barriers obtained, for cluster production on percolation lattices, from the Boltzmann factors show a power-law dependence on cluster size with an exponent of 0.42 +- 0.02. The EOS Au multifragmentation data yield barriers with a power-law exponent of 0.68 +- 0.03. Values of the surface energy coefficient of a low density nuclear system are also extracted.

Abstract:
The emission of clusters in the nuclear disassembly is investigated within the framework of isospin dependent lattice gas model and classical molecular dynamics model. As observed in the recent experimental data, it is found that the emission of individual cluster is poissonian and thermal scaling is observed in the linear Arrhenius plots made from the average multiplicity of each cluster. The mass, isotope and charge dependent "emission barriers" are extracted from the slopes of the Arrhenius plots and their possible physical implications are investigated.

Abstract:
Clusters in the three-dimensional Ising model rigorously obey reducibility and thermal scaling up to the critical temperature. The barriers extracted from Arrhenius plots depend on the cluster size as $B \propto A^{\sigma}$ where $\sigma$ is a critical exponent relating the cluster size to the cluster surface. All the Arrhenius plots collapse into a single Fisher-like scaling function indicating liquid-vapor-like phase coexistence and the univariant equilibrium between percolating clusters and finite clusters. The compelling similarity with nuclear multifragmentation is discussed.

Abstract:
To make a statement about the nature and mechanism of fragmentation, it is necessary to probe directly any competition, or lack thereof, between the emission of various particle species as a function of excitation energy. The task is then to find a global observable that best follows the increase in excitation energy or dissipated energy. In the following, we will consider two contradictory claims that have been advanced recently: 1) the claim for a predominantly dynamical fragment production mechanism; and 2) the claim for a dominant statistical and thermal process. We will present a new analysis in terms of Poissonian reducibility and thermal scaling, which addresses some of the criticisms of the binomial analysis.

Abstract:
Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. Using a procedure inspired by the similar, but continuous case of jet fragmentation in QCD, this discretized process may be analyzed into eigenmodes, corresponding to moments of the distribution of multiplicities. The orders of these moments are usually noninteger numbers. The resulting analysis can be made time independent and is applicable to various phenomenological multifragmentation processes, in which case it leads to new approximate finite-size scaling relations for the spectrum of fragments.

Abstract:
Using a combination of analytic arguments and numerical simulations, we determine lower and upper bounds for the energy barriers to the motion of a defect line in a random potential at low temperatures. We study the cases of magnetic flux lines in high-$T_{c}$ superconductors in 2 and 3 dimensions, and of domain walls in 2 dimensional random-field Ising models. The results show that, under fairly general conditions, energy barriers have the same scaling as the fluctuations in free energy, except for possible logarithmic factors. This holds not only for barriers between optimal configurations of the line, but also for barriers separating any metastable configuration from a configuration of minimal energy. Similar arguments may be applicable to other elastic media with impurities, such as bunches of flux lines.

Abstract:
An overview of the recent progress in the studies of nuclear multifragmentation is presented. Special emphasis is put on the exploration of isotopic trends in nuclear multifragmentation and the possibilities to extract physical information related to the nuclear equation of state. Relevant experimental methods of isotope identification are described. The isotopic composition of fragments is used to extract the values of thermodynamical observables of the system undergoing multifragmentation such as temperature and chemical potentials. Various methods for extraction of thermodynamical variables are analyzed. An overview of methods of isotope thermometry, exploring the sensitivity of various yield ratios to temperature, is presented. An exponential scaling of relative isotopic yields from reactions with different neutron content, called isoscaling, is used to explore the evolution of the isospin degrees of freedom of the system. Finally, the nuclear equation of state and the isospin-asymmetric liquid-gas phase transition in the nuclear matter are discussed.

Abstract:
For the statistical multifragmentation model the critical indices $\alpha^\prime, \beta, \gamma^\prime, \delta$ are calculated as functions of the Fisher parameter $\tau$. It is found that these indices have different values than in Fisher's droplet model. Some peculiarities of the scaling relations are discussed. The basic model predicts for the index $\tau$ a narrow range of values, $1.799< \tau < 1.846$, which is consistent with two experiments on nuclear multifragmentation.