Geometrically confined thermal field theory: Finite size corrections and phase transitions
| Autor: | Isobel Kolbé, S. Mogliacci, W. A. Horowitz |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Physics Phase transition Finite volume method Nuclear Theory Statistical Mechanics (cond-mat.stat-mech) Internal energy Thermal quantum field theory 010308 nuclear & particles physics Critical phenomena Mathematical analysis FOS: Physical sciences 01 natural sciences Heat capacity Ideal gas Nuclear Theory (nucl-th) High Energy Physics - Phenomenology High Energy Physics - Phenomenology (hep-ph) High Energy Physics - Theory (hep-th) Quantum Gases (cond-mat.quant-gas) 0103 physical sciences Condensed Matter - Quantum Gases 010306 general physics Scalar field Condensed Matter - Statistical Mechanics |
| Zdroj: | Physical Review |
| ISSN: | 2470-0029 2470-0010 |
| DOI: | 10.1103/physrevd.102.116017 |
| Popis: | Motivated by the recent shocking results from RHIC and LHC that show quark-gluon plasma signatures in small systems, we study a simple model of a massless, noninteracting scalar field confined with Dirichlet boundary conditions. We use this system to investigate the finite size corrections to thermal field theoretically derived quantities compared to the usual Stefan-Boltzmann limit of an ideal gas not confined in any direction. Two equivalent expressions with different numerical convergence properties are found for the free energy in $D$ rectilinear spacetime dimensions with $c\le D-1$ spatial dimensions of finite extent. We find that the First Law of Thermodynamics generalizes such that the pressure depends on direction but that the Third Law is respected. For systems with finite dimension(s) but infinite volumes, such as a field constrained between two parallel plates or a rectangular tube, the relative fluctuations in energy are zero, and hence the canonical and microcanonical ensembles are equivalent. We present precise numerical results for the free energy, total internal energy, pressure, entropy, and heat capacity of our field between parallel plates, in a tube, and in finite volume boxes of various sizes in 4 spacetime dimensions. For temperatures and system sizes relevant for heavy ion phenomenology, we find large deviations from the Stefan-Boltzmann limit for these quantities, especially for the pressure. Further investigation of an isolated system of fields constrained between parallel plates reveals a divergent isoenergetic compressibility at a critical length $L_c\sim1/T$. We have thus discovered a new second order phase transition via a first principles calculation, a transition that is driven by the size of the system. Comment: 47 pages, 15 figures |
| Databáze: | OpenAIRE |
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