Abstract: The dispersion relation of a monoatomic two-dimensional lattice with long-range interactions is derived according to the theory of lattice dynamics. Based on a simple harmonic approximation, a general dispersion relation that takes into account arbitrary neighbor interactions is obtained. The results of the nearest neighbor and the second nearest neighbor approximation are analyzed. When the order of the nearest neighbors p is large, the contribution of the pth nearest neighbors to the average vibration frequency in the Brillouin zone decays in a power law form with the increase of the neighbor number. Moreover, the long-range Coulomb interaction is analyzed as an example. Based on this microscopic dynamics, the effect of long-range interaction on macroscopic heat capacity is numerically investigated, and the heat capacity of the system decays in a power law form with the increase of the neighbor number.

Key words: lattice vibration, dispersion relation, harmonic approximation, periodic boundary conditions, square lattice, heat capacity