Glasslike properties of a chain of particles with anharmonic and competing interactions

For a translationally invariant model of a chain of classical particles with anharmonic and competing nearest- and next-nearest-neighbor interactions, the existence of an infinite number of metastable chaotic equilibrium configurations is proved. Their pair distribution function exhibits more or less pronounced nearest-, next-nearest-, etc., neighbor peaks and the absence of long-range order (under certain conditions). The structure factor shows beside the usual peaks a sequence of extra peaks. The existence of two-level systems for such chaotic configurations is proved. Their energies and the barrier heights are calculated exactly. The corresponding density of states is not constant and shows a scaling property which leads to a power law c(T)∼$T^{d̃}$ for the specific heat with a fractional exponent d̃={ln[$p^2$+(1-p${)}^2$]} /ln‖η‖, where 0<p<1 characterizes the type of disorder and η≶0 depends only on the ratio of the nearest- and next-nearest-neighbor coupling constants. A pair potential is given for which these results remain true.