Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase

•Spectral properties of the (2+1)(2+1)-dimensional Ising model were investigated.•Critical amplitude relations for the low-lying levels were calculated.•Connections with a Z2 gauge theory conjecture and with possible future experiments were made.•The numerical diagonalization method was employed.•Corrections to scaling were suppressed by extended interactions.

In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, m2