  The criticality between the nematic and valence-bond-solid (VBS) phases was
investigated for the two-dimensional quantum S=1-spin model with the three-spin
and biquadratic interactions by means of the numerical diagonalization method.
It is expected that the criticality belongs to a novel universality class, the
so-called deconfined criticality, accompanied with unconventional critical
indices. In this paper, we incorporate the three-spin interaction, and adjust
the (redundant) interaction parameter so as to optimize the finite-size
behavior. Treating the finite-size cluster with N \le 20 spins, we estimate the
correlation-length critical exponent as \nu=0.88 (3).
