Quantum lattice model with local multi-well potentials: Riemannian geometric interpretation for the phase transitions in ferroelectric crystals

Geometrical aspects of quantum lattice model with the local anharmonic potentials are presented for the case of deformed ferroelectric lattice. A metric is defined in a two-dimensional phase space of the dipole ordering or polarization ( η) vs. volume deformation (u). Based on the metric components,...

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Bibliographic Details
Published in:Physica A 2020-10, Vol.556, p.124837, Article 124837
Main Author: Erdem, Rıza
Format: Article
Language:English
Subjects:
Anharmonic potential
Ferroelectric crystals
formula omitted
Geometric phase diagram
Phase transitions
Quantum lattice model
Ricci scalar
Riemannian geometry
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Summary:Geometrical aspects of quantum lattice model with the local anharmonic potentials are presented for the case of deformed ferroelectric lattice. A metric is defined in a two-dimensional phase space of the dipole ordering or polarization ( η) vs. volume deformation (u). Based on the metric components, an expression for the thermodynamic Ricci curvature scalar (R) is derived in terms of the known equilibrium values of η and u introduced by Velychko and Stasyuk (2019). As an example, the calculated curvature in the ferroelectric phase of Sn2P2S6 crystal demonstrates negative value while positive curvature in the paraelectric phase is obtained. The presence of anomalies of R in the ferroelectric phase transition regime of the first- and second-order as well as the tricritical point is observed.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2020.124837