Analysis of equations of state and determination of the Grüneisen function for two-dimensional crystal lattices

The method of particle dynamics is used for both analytical and numerical investigation of tensor properties of the Mie–Gruneisen equation of state for two-dimensional solids with crystalline structure. It is demonstrated analytically that the Gruneisen function essentially depends on the ratio between the eigenvalues of the deformation temperature tensor, which, in this work, is determined numerically.