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The critical indices α', β, γ', and δ of the Quark Gluon Bags with Surface Tension Model that has a critical endpoint are calculated and compared with the exponents of other models. These indices are expressed in terms of the most general parameters of the model. Despite the usual expectations the found critical indices do not depend on the Fisher exponent τ and on the parameter [symbol: see text] which relates the mean bag surface to its volume. The scaling relations for the obtained critical exponents are verified, and it is demonstrated that for the standard definition of the index α' the Fisher and the Griffiths scaling inequalities are not fulfilled in general case, whereas the Liberman scaling inequality is always obeyed. This is not surprising for the phase diagram with the asymmetric properties of pure phases, but the present model also provides us with the first and explicit example that the specially defined index α'(s) does not recover the scaling relations as well. Therefore, here we suggest the physically motivated definition of the index α' = α'(c) and demonstrate that such a definition recovers the Fisher scaling inequality, while it is shown that the Griffiths inequality should be generalized for the phase diagram with the asymmetric properties. The critical exponents of several systems that belong to different universality classes are successfully described by the parameters of the present model, and hence its equation of state can be used for a variety of practical applications.

The surface partition of large clusters is derived analytically for a simple statistical model by using the Laplace-Fourier transformation method. In the limit of small amplitude deformations, a suggested "hills and dales model" reproduces the leading term of the Fisher result for the surface entropy to within a few percent. The model also gives the degeneracy prefactor of large clusters. The surface partition of finite clusters is also discussed.

The effects of the finite size of a liquid drop undergoing a phase transition are described in terms of the complement, the largest (but mesoscopic) drop representing the liquid in equilibrium with the vapor. Vapor cluster concentrations, pressure, and density from fixed mean density lattice gas (Ising) calculations are explained in terms of the complement generalization of Fisher's model. Accounting for this finite size effect is important for extracting the infinite nuclear matter phase diagram from experimental data.

The relativistic kinetic equations for two domains separated by a hypersurface with both spacelike and timelike parts are derived. The particle exchange between the domains separated by timelike boundaries generates source terms and modifies the collision term of the kinetic equation. The correct hydrodynamic equations for the "hydro+cascade" models are obtained and their differences from existing freeze-out models of the hadronic matter are discussed.

The transverse mass spectra of Omega, J/psi, and psi' in Pb+Pb collisions at 158A GeV are studied within a hydrodynamical model of the quark-gluon-plasma expansion and hadronization. The model reproduces the existing data with the common hadronization parameters: temperature T = T(H) congruent with 170 MeV and average collective transverse velocity v(T) congruent with 0.2.