Although widely studied experimentally in the 1990s, the structure and properties of low-dimensional or high-pressure phases of fullerenes have recently been re-examined. Remarkably, recent experiments have shown that transparent, nearly pure amorphous sp3-bonded carbon phases can be obtained by heating a C60 molecular crystal at a high pressure. With the additional aim of testing the ability of three classical carbon potentials reactive empirical bond order, environment-dependent interatomic potential, and reactive force-field to reproduce these results, we investigate the details of the structural transformations undergone by fullerene crystals over a wide range of pressures and temperatures. All the potentials tested show that the initial polymerization of fullerenes is accompanied by negative thermal expansion, albeit in slightly different ranges. However, more significant differences in structural and mechanical properties are observed in the amorphous phases, in particular the sp3 carbon fraction and the existence of layered amorphous carbon. Overall, these results indicate to which extent classical reactive potentials can be used to explore phase transitions over a wide range of pressures and temperatures.