Shape descriptors of equilibrium states in a quantum lattice model with local multi-well potentials: A geometric analysis near the phase transitions in Sn<sub>2</sub>P<sub>2</sub>S<sub>6</sub> ferroelectric crystal

We analyze the equilibrium states of quantum lattice model with local multi-well potentials for Sn2P2S6 ferroelectric crystals using the mean and Gaussian curvatures (H, K), curvedness (C) and shape index (S). From the energy gap, pressure and temperature variations of H, K, C and S, we have reported the geometric construction of the free energy surfaces for the ferroelectric and paraelectric phases. Their behaviors are explicitly observed near the ferroelectric-paraelectric phase transitions. It is found that H, C and S display a cusp singularity at the criticality while K converges to zero on both sides of the critical and tricritical points.