  Thermal transport in solids changes its nature from phonon propagation that
suffers from perturbative scattering to thermally activated hops between
localized vibrational modes as the level of disorder increases. Models have
been proposed to understand these two distinct extremes that predict opposite
temperature dependence of the thermal conductivity, but not for the transition
or the intermediate regime. Here we explore thermal transport in
two-dimensional crystalline and amorphous silica with varying levels of
disorder, {\alpha}, by performing atomistic simulations as well as analysis
based on the kinetic and Allen-Feldman theories. We demonstrate the crossover
between the crystalline and amorphous regimes at {\alpha} ~ 0.3, which can be
identified by a turnover of the temperature dependence in thermal conductivity,
and explained by the dominance of thermal hopping processes. The determination
of this critical disorder level is also validated by the analysis of the
participation ratio of localized vibrational modes, and the spatial
localization of heat flux. These factors can serve as key indicators in
characterizing the transition in heat transport mechanisms.
