Nonlinear Elasticity of the Phase Field Crystal Model from the Renormalization Group

TL;DR

This paper derives a nonlinear elastic response model for the phase field crystal using renormalization group equations, connecting density wave amplitudes to strain and effective free energy.

Contribution

It introduces a new derivation of the nonlinear elasticity of the phase field crystal from renormalization group equations, linking density waves to strain-based free energy.

Findings

Derived a free energy as a function of strain tensor

Established equations for nonlinear elastic response

Connected renormalization group equations to elasticity

Abstract

The rotationally-covariant renormalization group equations of motion for the density wave amplitudes in the phase field crystal model are shown to follow from a dynamical equation driven by an effective free energy density that we derive. We show that this free energy can be written purely as a function of the strain tensor and thence derive the corresponding equations governing the nonlinear elastic response.