Numerical studies of the extended two-chain model of friction

We investigate numerically a simple microscopic model to describe wearless dry friction between atomically flat contact interfaces without thermal fluctuations (T=0K). The analysis of the incommensurate ground state shows a breaking of analyticity when the amplitude $ϵ$ of the Lennard-Jones interaction between the both harmonic chains increased beyond a critical value ${ϵ}_c$. By the introduction of a suitable order parameter and using a finite size scaling we could show that the breaking of analyticity is a second order phase transition. This transition is often called Aubry transition. By applying of an uniform external force $F^{ex}$ we have determined the critical force of static friction $F_c$ above a sliding motion occurs.