Universal critical behavior of the two-magnon-bound-state mass gap for the -dimensional Ising model

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 ≤ 20 spins indicates the mass-gap ratio m 2 / m 1 = 1.84 ( 1 ) .