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 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 the numerical diagonalization for finite clusters with N \le 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).

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• Universal critical behavior of the two-magnon-bound-state mass gap for the (2+1)-dimensional Ising model
• Criticality of the (2+1)-dimensional S=1 transverse-field Ising model with extended interactions: Suppression of corrections to scaling
• Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase
• Hierarchy of the low-lying excitations for the $(2+1)$-dimensional $q=3$ Potts model in the ordered phase