Universal critical behavior of the two-magnon-bound-state mass gap for the (2 + 1) -dimensional Ising model

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5 Citations (Scopus)

Abstract

The two-magnon-bound-state mass gap m2 for the two-dimensional quantum Ising model was investigated by means of the numerical diagonalization method; the low-lying spectrum is directly accessible via the numerical diagonalization method. It has been claimed that the ratio m2/ m1 (m1: one-magnon mass gap) is a universal constant in the vicinity of the critical point. Aiming to suppress corrections to scaling (lattice artifact), we consider the spin-S=1 Ising model with finely-adjusted extended interactions. The simulation result for the finite-size cluster with N≤20 spins indicates the mass-gap ratio m2/m11.84(1).

Original languageEnglish
Pages (from-to)577-582
Number of pages6
JournalPhysica A: Statistical Mechanics and its Applications
Volume413
DOIs
Publication statusPublished - Nov 1 2014

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Critical Behavior
Bound States
Ising model
Ising Model
Diagonalization
Corrections to Scaling
artifacts
Critical point
critical point
scaling
Interaction
Simulation
simulation
interactions

Keywords

  • Amplitude relation
  • Ising model
  • Magnon bound state
  • Numerical diagonalization method
  • Quantum phase transition
  • Three-dimensional-Ising universality

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistics and Probability

Cite this

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abstract = "The two-magnon-bound-state mass gap m2 for the two-dimensional quantum Ising model was investigated by means of the numerical diagonalization method; the low-lying spectrum is directly accessible via the numerical diagonalization method. It has been claimed that the ratio m2/ m1 (m1: one-magnon mass gap) is a universal constant in the vicinity of the critical point. Aiming to suppress corrections to scaling (lattice artifact), we consider the spin-S=1 Ising model with finely-adjusted extended interactions. The simulation result for the finite-size cluster with N≤20 spins indicates the mass-gap ratio m2/m11.84(1).",
keywords = "Amplitude relation, Ising model, Magnon bound state, Numerical diagonalization method, Quantum phase transition, Three-dimensional-Ising universality",
author = "Yoshihiro Nishiyama",
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AB - The two-magnon-bound-state mass gap m2 for the two-dimensional quantum Ising model was investigated by means of the numerical diagonalization method; the low-lying spectrum is directly accessible via the numerical diagonalization method. It has been claimed that the ratio m2/ m1 (m1: one-magnon mass gap) is a universal constant in the vicinity of the critical point. Aiming to suppress corrections to scaling (lattice artifact), we consider the spin-S=1 Ising model with finely-adjusted extended interactions. The simulation result for the finite-size cluster with N≤20 spins indicates the mass-gap ratio m2/m11.84(1).

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KW - Three-dimensional-Ising universality

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