  We study numerically the critical region and the disordered phase of the
random transverse-field Ising chain. By using a mapping of Lieb, Schultz and
Mattis to non-interacting fermions, we can obtain a numerically exact solution
for rather large system sizes, $L \le 128$. Our results confirm the striking
predictions of earlier analytical work and, in addition, give new results for
some probability distributions and scaling functions.
