Dynamical Behaviour of Low Autocorrelation Models

Abstract

We have investigated the nature of the dynamical behaviour in low autocorrelation binary sequences. These models do have a glass transition $T_G$ of a purely dynamical nature. Above the glass transition the dynamics is not fully ergodic and relaxation times diverge like a power law $τ\sim (T-T_G)^{-γ}$ with $γ$ close to $2$. Approaching the glass transition the relaxation slows down in agreement with the first order nature of the dynamical transition. Below the glass transition the system exhibits aging phenomena like in disordered spin glasses. We propose the aging phenomena as a precise method to determine the glass transition and its first order nature.