Before revision:  For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of O(\log n) and \Omega(\log n/\log\log n) for \alpha=2 and \Theta(n^{ 1-\alpha/ 2  }) for \alpha<2 respectively.
After revision:  For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of O(\log n) and \Omega(\log n/\log\log n) for \alpha=2 and \Theta(n^{ 2 }) for \alpha<2 respectively.