Glass transition and rigidity in the aging linear harmonic oscillator model

Abstract Rigidity theory in glasses was originally formulated to understand the relationship between network topology and glass forming ability, the later given by the minimal cooling rate required to form a glass. Here a study is presented on the glass transition temperature, specific heat and cooling/heating rate in a simple solvable low-temperature Monte Carlo Keating-like oscillator model. For a fixed heating rate, the results indicate that the glass transition temperature grows with the number of constraints as observed in real experiments. Moreover, to achieve glass transition, higher heating rates are needed as the number of constraints is decreased. These results are traced back to the high number of low-entropic energy barriers seen in flexible systems. Also, from the model, the fragility index is obtained and it shows an intermediate isostatically rigid phase which agrees, in a qualitatively level, with the experimental and computational evidence in some glasses.