  The two-magnon-bound-state mass gap m_2 for the two-dimensional quantum Ising
model was investigated by means of the numerical diagonalization method; the
low-lying spectrum is directly accessible via the numerical diagonalization
method. It has been claimed that the ratio m_2/m_1 (m_1: one-magnon mass gap)
is a universal constant in the vicinity of the critical point. Aiming to
suppress corrections to scaling (lattice artifact), we consider the spin-S=1
Ising model with finely-adjusted extended interactions. The simulation result
for the finite-size cluster with N \le 20 spins indicates the mass-gap ratio
m_2/m_1=1.84(1).
