Model for a glassy adsorbate: Two-level systems and specific heat

A two-dimensional Frenkel-Kontorova model with piecewise harmonic substrate potential is used to investigate the properties of a glassy adsorbed layer of atoms interacting via harmonic nearest-neighbor forces. An infinite number of metastable configurations is found. Under certain conditions these are in a one-to-one correspondence to a class of sequences of integers (symbols) in analogy to chaotic dynamical systems also demonstrating the possibility of two-dimensional spatial chaos. A microscopic derivation of the simplest two-level systems is given. Their asymmetries, potential barriers, and density of states are determined analytically. We have found that the density of states depends sensitively on type and degree of the disorder of the adsorbed layer. For quasi-one-dimensional disorder produced by ‘‘kink’’ defects, earlier results for a one-dimensional model are reproduced, leading for the specific heat to a power law c(T)∼$T^d$̃ with a fractional exponent smaller than 1. On the other hand, for ‘‘Gaussian’’ disorder obtained from an idealized quenching process, we find a constant density of states and therefore a linear specific heat, provided the quenching temperature $T_{\mathrm{qu}}$ is sufficiently high. For decreasing $T_{\mathrm{qu}}$ the density of states becomes nonconstant, developing structures on any energy scale. Furthermore, we show the time dependence of the specific heat to be exponential.