Bound-state energy of the three-dimensional Ising model in the broken-symmetry phase: suppressed finite-size corrections.
The low-lying spectrum of the three-dimensional Ising model is investigated numerically; we made use of an equivalence between the excitation gap and the reciprocal correlation length. In the broken-symmetry phase, the magnetic excitations are attractive, forming a bound state with an excitation gap m_{2} (<2m_{1}) ( m_{1} : elementary excitation gap). It is expected that the ratio m_{2}/m_{1} is a universal constant in the vicinity of the critical point. In order to estimate m_{2}/m_{1} , we perform a numerical diagonalization for finite clusters with N < or = 15 spins. In order to reduce the finite-size errors, we incorporated the extended (next-nearest-neighbor and four-spin) interactions. As a result, we estimate the mass-gap ratio as m_{2}/m_{1}=1.84(3) .
Nishiyama
Yoshihiro
Y
Department of Physics, Faculty of Science, Okayama University, Okayama 700-8530, Japan.