### Abstract

In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, m_{2}<m_{3}<…. Each ratio m_{2,3,…}/m_{1} (m_{1}: 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 m_{2,3,4}, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.

Original language | English |
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Pages (from-to) | 303-309 |

Number of pages | 7 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 463 |

DOIs | |

Publication status | Published - Dec 1 2016 |

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### 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

**Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase.** / Nishiyama, Yoshihiro.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase

AU - Nishiyama, Yoshihiro

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

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.

KW - Exact diagonalization method

KW - Magnon mass gaps

KW - Two-dimensional transverse-field Ising model

KW - Universal amplitude ratio

UR - http://www.scopus.com/inward/record.url?scp=84982671700&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84982671700&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2016.07.045

DO - 10.1016/j.physa.2016.07.045

M3 - Article

AN - SCOPUS:84982671700

VL - 463

SP - 303

EP - 309

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -