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:
We explore the natural limit of binomial reducibility in nuclear multifragmentation by constructing excitation functions for intermediate mass fragments (IMF) of a given element Z. The resulting multiplicity distributions for each window of transverse energy are Poissonian. Thermal scaling is observed in the linear Arrhenius plots made from the average multiplicity of each element. ``Emission barriers'' are extracted from the slopes of the Arrhenius plots and their possible origin is discussed.

Abstract:
We develop an improved Statistical Multifragmentation Model that provides the capability to calculate calorimetric and isotopic observables with precision. With this new model we examine the influence of nuclear isospin on the fragment elemental and isotopic distributions. We show that the proposed improvements on the model are essential for studying isospin effects in nuclear multifragmentation. In particular, these calculations show that accurate comparisons to experimental data require that the nuclear masses, free energies and secondary decay must be handled with higher precision than many current models accord.

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:
Motivated by the decade-long debate over the issue of criticality supposedly observed in nuclear multifragmentation, we propose a dynamical lattice model to simulate the phenomenon. Its Ising Hamiltonian mimics a short range attractive interaction which competes with a thermal-like dissipative process. The results here presented, generated through an event-by-event analysis, are in agreement with both experiment and those produced by a percolative (non-dynamical) model.

Abstract:
A systematic study of the effect of fragment$-$fragment interaction, quantum statistics, $\gamma$-feeding and collective flow is made in the extraction of the nuclear temperature from the double ratio of the isotopic yields in the statistical model of one-step (Prompt) multifragmentation. Temperature is also extracted from the isotope yield ratios generated in the sequential binary-decay model. Comparison of the thermodynamic temperature with the extracted temperatures for different isotope ratios show some anomaly in both models which is discussed in the context of experimentally measured caloric curves.

Abstract:
Deviations from an idealized equilibrium phase transition picture in nuclear multifragmentation is studied in terms of the entropic index. We investigate different heat-capacity features in the canonical quantum statistical model of nuclear multifragmentation generalized in the framework of Tsallis nonextensive thermostatistics. We find that the negative branch of heat capacity observed in quasi-peripheral Au+Au collisions is caused primarily by the non-generic nonextensivity effects.

Abstract:
The multifragmentation of excited spherical nuclear sources with various N/Z ratios and fixed mass number is studied within dynamical and statistical models. The dynamical model treats the multifragmentation process as a final stage of the growth of density fluctuations in unstable expanding nuclear matter. The statistical model makes a choice of the final multifragment configuration according to its statistical weight at a global thermal equilibrium. Similarities and differences in the predictions of the two models on the isotopic composition of the produced fragments are presented and the most sensitive observable characteristics are discussed.

Abstract:
Because of thermal expansion and residual interactions, hot nuclear fragments produced in multifragmentation reactions may have lower nucleon density than the equilibrium density of cold nuclei. In terms of liquid-drop model this effect can be taken into account by reducing the bulk energy of fragments. We study the influence of this change on fragment yields and isotope distributions within the framework of the statistical multifragmentation model. Similarities and differences with previously discussed modifications of symmetry and surface energies of nuclei are analyzed.

Abstract:
Using a recently proposed classification scheme for phase transitions in finite systems [Phys.Rev.Lett.{\bf 84},3511 (2000)] we show that within the statistical standard model of nuclear multifragmentation the predicted phase transition is of first order.