Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions
Feb 17, 202019 pages
Published in:
- Entropy 22 (2020) 4, 380
- Published: Mar 26, 2020
e-Print:
- 2002.06986 [cond-mat.stat-mech]
DOI:
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Abstract: (MDPI)
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of ϕ 4 models with either nearest-neighbours and mean-field interactions.- microcanonical ensemble
- phase transitions
- differential geometry
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