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

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  • Erdem, Rıza

Abstract

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.

Suggested Citation

  • Erdem, Rıza, 2020. "Quantum lattice model with local multi-well potentials: Riemannian geometric interpretation for the phase transitions in ferroelectric crystals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    • Handle: RePEc:eee:phsmap:v:556:y:2020:i:c:s0378437120304349
    DOI: 10.1016/j.physa.2020.124837
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