Exactly Solvable Models: The Road towards a Rigorous Treatment of Phase Transitions in Finite Nuclear Systems

Source: arXiv

ABSTRACT We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical multifragmentation model, the Gas of Bags Model and the Hills and Dales Model of surface partition. Thus, the Laplace-Fourier transform allows one to study the nuclear matter equation of state, the equation of state of hadronic and quark gluon matter and surface partitions on the same footing. A complete analysis of the isobaric partition singularities of these models is done for finite systems. The developed formalism allows us, for the first time, to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics and demonstrate the pitfalls of earlier works. The found solutions may be used for building up a new theoretical apparatus to rigorously study phase transitions in finite systems. The strategic directions of future research opened by these exact results are also discussed. Comment: 26 pages

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The many-body cluster-interaction model introduced in the first part is studied in its critical region for a range of special potentials, principally: “model (A)” which is characterized by a “surface” exponent and a “geometric” exponent, τc. It is shown that the vapor pressure curve pσ(T) may exhibit “maxithermal” and “maxibaric” points where is ∞ or 0, respectively. The coexistence curves may be flat-topped (τc > 2), rounded on the gas-like side (2 > τc > 2 − σ), or cuspoidal (2 − σ > τc > 1) so that as T → Tc. For model (A), the asymptotic approach to the critical point of the coexistence curve, the specific heat, the compressibility, etc. (for the gas-like phase) is found to be described by the usual critical exponents (at least with regard to the singular parts of these functions). Furthermore, the gas-like phase Gibbs free energy in the whole critical region is shown to satisfy a scaling equation in terms of two special coordinates (ξ and θ) which are both linear combinations of (p−pc) and (T − Tc). Nevertheless, the critical exponents on the critical isochore (v = vc, T ⩾ Tc) do not, in general, satisfy the normal exponent relations: it is found that γ < γ′ while, in most cases, α′ ⩽ α ⩽ 0. It is noted that the droplet picture of condensation corresponds closely to τc > 2 and also scales. Finally, the “mechanism” of the model is exhibited in more detail by studying the statistics of the clusters: their size, length, etc.
    Annals of Physics 05/1970; 58(1):217–267. DOI:10.1016/0003-4916(70)90244-7 · 3.07 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this article I introduce aspects of current theory used to interpret the preliminary data on ultra-relativistic nuclear collisions at RHIC energies in terms of the physical properties of QCD matter at extreme densities. Topics covered include: What are the physics questions at SPS and RHIC? Geometrical vs. dynamical features of A+A. The interplay of computable hard perpurbative QCD vs. phenomenological soft dynamics. Baryon number transport and junctions. How can we compute and get experimental control over the initial conditions? How to reconcile apparent hydrodynamic behavior with partonic/hadronic transport theory? I use the preliminary RHIC data available up to June 1, 2001 to illustrate these topics. Most technical details are deferred to the literature. However, since the main new observable at RHIC relative to SPS is jet quenching, I elaborate more on this "tomographic" probe of ultra-dense matter. The possible discovery of jet quenching at RHIC by STAR and PHENIX is highlighted.
    Lecture Notes in Physics 01/2002; 583:37. DOI:10.1142/9789812702845_0025
  • [Show abstract] [Hide abstract]
    ABSTRACT: Unlike most other texts on the subject, this clear, concise introduction to the theory of microscopic bodies treats the modern theory of critical phenomena. Provides up-to-date coverage of recent major advances, including a self-contained description of thermodynamics and the classical kinetic theory of gases, interesting applications such as superfluids and the quantum Hall effect, several current research applications, The last three chapters are devoted to the Landau-Wilson approach to critical phenomena. Many new problems and illustrations have been added to this edition.


Available from