### Abstract

We consider the paramagnetic phase of the random transverse-field Ising spin chain and study the dynamical properties by numerical methods and scaling considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to new quantities, such as the nonlinear susceptibility, higher excitations, and the energy-density autocorrelation function. We show that in the Griffiths phase all the above quantities exhibit power-law singularities and the corresponding critical exponents, which vary with the distance from the critical point, can be related to the dynamical exponent z, the latter being the positive root of [(J/h)^{1/z}]_{av}= 1. Particularly, whereas the average spin autocorrelation function in imaginary time decays as [G]_{av}(τ)∼τ^{-1/z} the average energy-density autocorrelations decay with another exponent as [G^{e}]_{av}(τ)∼τ^{-2-1/z}.

Original language | English |
---|---|

Pages (from-to) | 11308-11314 |

Number of pages | 7 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 59 |

Issue number | 17 |

Publication status | Published - 1999 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*59*(17), 11308-11314.

**Griffiths-McCoy singularities in the random transverse-field Ising spin chain.** / Iglói, F.; Juhász, Róbert; Rieger, Heiko.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 59, no. 17, pp. 11308-11314.

}

TY - JOUR

T1 - Griffiths-McCoy singularities in the random transverse-field Ising spin chain

AU - Iglói, F.

AU - Juhász, Róbert

AU - Rieger, Heiko

PY - 1999

Y1 - 1999

N2 - We consider the paramagnetic phase of the random transverse-field Ising spin chain and study the dynamical properties by numerical methods and scaling considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to new quantities, such as the nonlinear susceptibility, higher excitations, and the energy-density autocorrelation function. We show that in the Griffiths phase all the above quantities exhibit power-law singularities and the corresponding critical exponents, which vary with the distance from the critical point, can be related to the dynamical exponent z, the latter being the positive root of [(J/h)1/z]av= 1. Particularly, whereas the average spin autocorrelation function in imaginary time decays as [G]av(τ)∼τ-1/z the average energy-density autocorrelations decay with another exponent as [Ge]av(τ)∼τ-2-1/z.

AB - We consider the paramagnetic phase of the random transverse-field Ising spin chain and study the dynamical properties by numerical methods and scaling considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to new quantities, such as the nonlinear susceptibility, higher excitations, and the energy-density autocorrelation function. We show that in the Griffiths phase all the above quantities exhibit power-law singularities and the corresponding critical exponents, which vary with the distance from the critical point, can be related to the dynamical exponent z, the latter being the positive root of [(J/h)1/z]av= 1. Particularly, whereas the average spin autocorrelation function in imaginary time decays as [G]av(τ)∼τ-1/z the average energy-density autocorrelations decay with another exponent as [Ge]av(τ)∼τ-2-1/z.

UR - http://www.scopus.com/inward/record.url?scp=0001056711&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001056711&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001056711

VL - 59

SP - 11308

EP - 11314

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 17

ER -