Bound-state energy of the d=3 Ising model in the broken-symmetry phase: Suppressed finite-size corrections
Abstract
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 m2(<2m1) (m1: elementary excitation gap). It is expected that the ratio m2/m1 is a universal constant in the vicinity of the critical point. In order to estimate m2/m1, we perform the numerical diagonalization for finite clusters with N 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 m2/m1=1.84(3).
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