It would be incredibly unlikely that each core could directly access the full 620TB. The current largest machines on the Top500 list are all distributed memory machines(clusters). However, the trends in modern interconnect networks are to increase the capabilities for doing stuff like remote direct memory access (RDMA). In such a scheme, the remote memory is not addressable(with load/store instructions), but stuff can be transferred between memories of different nodes by the network hardware. The codes commonly run on the top500 machines are likely written in MPI or MPI/OpenMP. This means they don't need to directly access remote memories.