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arXiv · 0804.1586

Bound-state energy of the d=3 Ising model in the broken-symmetry phase: Suppressed finite-size corrections

Yoshihiro Nishiyama
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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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Yoshihiro Nishiyama. 2008-04-09. Bound-state energy of the d=3 Ising model in the broken-symmetry phase: Suppressed finite-size corrections. https://doi.org/10.1103/physreve.77.051112

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