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The amorphous carbon-based resistive memory has recently attained vast attention due to its non-volatility, fast switching speed, long data retention, and multilevel recording. However, the memory switching mechanism of amorphous carbon media remains mysterious and thus severely restricted its application prospect. To resolve this issue, a comprehensive three-dimensional model by simultaneously solving the current continuity equation, heat transfer equation, and mass concentration equation, is developed to model the physical conversions between sp² and sp³ clusters. According to simulations, electric field was considered as the sole critical factor that determines the formation of conductive sp² filament during the `SET' process, whereas the `RESET' process is mainly attributed to the induced high temperature that accelerates the growth of sp³ cluster and causes the rupture of the sp² filament. It was additionally found that the sp² filament was preferably formed inside the region having larger sp² concentrations, and its rupture usually initiates from the filament center. The threshold voltages of carbon resistive memory for different thickness and different sp² fractions were also calculated and exhibited good agreement with experimental measurements.