  We study collective behavior of locally-coupled limit-cycle oscillators with
scattered intrinsic frequencies on $d$-dimensional lattices. A linear analysis
shows that the system should be always desynchronized up to $d=4$. On the other
hand, numerical investigation for $d= 5$ and 6 reveals the emergence of the
synchronized (ordered) phase via a continuous transition from the fully random
desynchronized phase. This demonstrates that the lower critical dimension for
the phase synchronization in this system is $d_{l}=4$
