Shape descriptors of equilibrium states in a quantum lattice model with local multi-well potentials: A geometric analysis near the phase transitions in Sn$_2$P$_2$S$_6$ ferroelectric crystals

TL;DR

This paper uses geometric shape descriptors to analyze equilibrium states in a quantum lattice model of ferroelectric crystals, revealing critical behaviors near phase transitions.

Contribution

It introduces a geometric approach using curvatures and shape indices to characterize phase transitions in a quantum lattice model.

Findings

Shape index shows cusp singularity at criticality

Gaussian curvature converges to zero near critical points

Energy surface geometry changes markedly at phase transitions

Abstract

We analyze the equilibrium states of quantum lattice model with local multi-well potentials for Sn$_2$P$_2$S$_6$ 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.