Universality in the Frenkel-Kontorova model with a cosh-type interaction

Abstract

We have studied a generalized Frenkel-Kontorova model with a cosh-type interaction. A distinctive feature of the model is that the winding number of the last Kolmogorov-Arnold-Moser torus could deviate from the golden mean value for a very large degree of nonlinearity. The singularity spectrum and the generalized fractal dimension depend on the nonlinearity spectrum. However, the critical exponents of the gap in the phonon spectrum, the correlation length, and the Peierls-Nabarro barrier are found to be the same as those found in the standard and Toda Frenkel-Kontorova models. Our conclusions agree with previous findings. {copyright} {ital 1997} {ital The American Physical Society}