Tunneling Levels and Specific Heat of One-Dimensional Chaotic Configurations

For a translationally invariant model of a chain of classical particles with competing interactions, the existence of tunneling levels is proved. Their density of states, which exhibits a scaling property, is derived for a special type of quenched disorder. Finally it is shown that the low-temperature specific heat behaves like $c\mathrm{}\left(T\right)\mathrm{}\sim T^{\tilde{d}}$ with a fractional exponent $\tilde{d}=\frac{-\left(\ln 2\right)}{\ln \left|\eta \right|}<1\mathrm{}$, where $\eta$ depends on the coupling constants.