Chaotic and regular behavior in two-dimensional anharmonic crystal lattices

A two-dimensional anharmonic lattice model to describe the behavior of coupled nonlinear displacement modes is constructed. The equations of motion and the underlying Hamiltonian of the anharmonic lattice are found. The equations of motion are analyzed using the fourth-order Runge-Kutta method. The integrability of the system is found to depend on its energy as well as the regularity of the system potential. A continuous transition between regular and chaotic behavior is found and is illustrated using Poincare´ sections. As an example, the effects of ordering on a (100) tungsten surface are discussed in this context.