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

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.

Contribution to the ``World Consensus Initiative III, Texas A & M University, College Station, Texas, USA, February 11-17, 2005, 21p

References in corpus (7)

• Critical line of the deconfinement phase transition
• The complement: a solution to liquid drop finite size effects in phase transitions
• The Van-der-Waals Gas EOS for the Lorentz Contracted Spheres
• Surface Partition of Large Fragments
• The Hagedorn thermostat
• Hagedorn Thermostat: A Novel View of Hadronic Thermodynamics
• Exact Analytical Solution of the Constrained Statistical Multifragmentation Model

Cited by in corpus (14)

• The statistical multifragmentation model for liquid-gas phase transition with a compressible nuclear liquid
• The Flow Constraint Influence on the Properties of Nuclear Matter Critical Endpoint
• Fresh look at the Hagedorn mass spectrum as seen in the experiments
• Quark Gluon Bags as Reggeons
• Exactly Solvable Model for the QCD Tricritcal Endpoint
• On Relation Between the Quark Gluon Bag Surface Tension and the Colour Tube String Tension
• Hard-core Radius of Nucleons within the Induced Surface Tension Approach
• The critical indices of the Quark-Gluon Bags with Surface Tension Model with tricritical endpoint
• Effects of Induced Surface Tension in Nuclear and Hadron Matter
• Is bimodality a sufficient condition for a first order phase transition existence?
• Exploring an Origin of the QCD Critical Endpoint
• Physical properties of Polyakov loop geometrical clusters in SU(2) gluodynamics
• Branching random graph model of rough surfaces describes thermal properties of the effective molecular potential
• Probing the tricritical endpoint of QCD phase diagram at NICA-FAIR energies