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

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1 Citation (Scopus)

Abstract

In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, m2<m3<…. Each ratio m2,3,…/m1 (m1: the single-magnon mass) is expected to be a universal constant in the vicinity of the critical point. In this paper, we devote ourselves to the (2+1)-dimensional counterpart, for which the universal hierarchical character remains unclear. We employed the exact diagonalization method, which enables us to calculate the dynamical susceptibility via the continued-fraction expansion. Thereby, we observe a variety of signals including m2,3,4, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.

Original languageEnglish
Pages (from-to)303-309
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume463
DOIs
Publication statusPublished - Dec 1 2016

Fingerprint

Bound States
Ising model
Ising Model
hierarchies
Transverse
Continued Fraction Expansion
Ferromagnet
Diagonalization
Finite-size Scaling
Ising
Susceptibility
magnons
Critical point
critical point
magnetic permeability
scaling
Calculate
expansion
Series
estimates

Keywords

  • Exact diagonalization method
  • Magnon mass gaps
  • Two-dimensional transverse-field Ising model
  • Universal amplitude ratio

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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title = "Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase",
abstract = "In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, m23<…. Each ratio m2,3,…/m1 (m1: the single-magnon mass) is expected to be a universal constant in the vicinity of the critical point. In this paper, we devote ourselves to the (2+1)-dimensional counterpart, for which the universal hierarchical character remains unclear. We employed the exact diagonalization method, which enables us to calculate the dynamical susceptibility via the continued-fraction expansion. Thereby, we observe a variety of signals including m2,3,4, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.",
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AB - In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, m23<…. Each ratio m2,3,…/m1 (m1: the single-magnon mass) is expected to be a universal constant in the vicinity of the critical point. In this paper, we devote ourselves to the (2+1)-dimensional counterpart, for which the universal hierarchical character remains unclear. We employed the exact diagonalization method, which enables us to calculate the dynamical susceptibility via the continued-fraction expansion. Thereby, we observe a variety of signals including m2,3,4, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.

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