dorsal/arxiv
View SchemaExactly Solvable Models: The Road Towards a Rigorous Treatment of Phase Transitions in Finite Systems
| Authors | K. A. Bugaev |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0511031 |
| URL | https://arxiv.org/abs/nucl-th/0511031 |
| DOI | 10.1134/S1063779607040028 |
| Journal | Phys.Part.Nucl.38:447-468,2007 |
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.
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"abstract": "We discuss exact analytical solutions of a variety of statistical models\nrecently obtained for finite systems by a novel powerful mathematical method,\nthe Laplace-Fourier transform. Among them are a constrained version of the\nstatistical multifragmentation model, the Gas of Bags Model and the Hills and\nDales Model of surface partition. Thus, the Laplace-Fourier transform allows\none to study the nuclear matter equation of state, the equation of state of\nhadronic and quark gluon matter and surface partitions on the same footing. A\ncomplete analysis of the isobaric partition singularities of these models is\ndone for finite systems. The developed formalism allows us, for the first time,\nto exactly define the finite volume analogs of gaseous, liquid and mixed phases\nof these models from the first principles of statistical mechanics and\ndemonstrate the pitfalls of earlier works. The found solutions may be used for\nbuilding up a new theoretical apparatus to rigorously study phase transitions\nin finite systems. The strategic directions of future research opened by these\nexact results are also discussed.",
"arxiv_id": "nucl-th/0511031",
"authors": [
"K. A. Bugaev"
],
"categories": [
"nucl-th"
],
"doi": "10.1134/S1063779607040028",
"journal_ref": "Phys.Part.Nucl.38:447-468,2007",
"title": "Exactly Solvable Models: The Road Towards a Rigorous Treatment of Phase Transitions in Finite Systems",
"url": "https://arxiv.org/abs/nucl-th/0511031"
},
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