Deadlock occurs when process 0 sends to process 1 while process 1 sends to process 0 simultaneously; both block waiting for a receive that never comes.

// deadlock: both processes block on MPI_Send waiting for the other to MPI_Recv
MPI_Send(buf, N, MPI_DOUBLE, peer, 0, MPI_COMM_WORLD);
MPI_Recv(buf, N, MPI_DOUBLE, peer, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);

The standard fixes are: use MPI_Sendrecv, which handles ordering internally; post a non-blocking MPI_Isend first, then MPI_Recv, then MPI_Wait; or alternate send/receive order by rank so even-rank processes send first and odd-rank processes receive first. Whether MPI_Send actually blocks depends on the implementation's internal buffer size, so relying on it to absorb a large message is non-portable and can silently deadlock on a different machine.