### Abstract

We study XY and dimerized XX spin-1/2 chains with random exchange couplings by analytical and numerical methods and scaling considerations. We extend previous investigations to dynamical properties, to surface quantities, and operator profiles, and give a detailed analysis of the Griffiths phase. We present a phenomenological scaling theory of average quantities based on the scaling properties of rare regions, in which the distribution of the couplings follows a surviving random-walk character. Using this theory we have obtained the complete set of critical decay exponents of the random XY and XX models, both in the volume and at the surface. The scaling results are confirmed by numerical calculations based on a mapping to free fermions, which then lead to an exact correspondence with directed walks. The numerically calculated critical operator profiles on large finite systems (L≤512) are found to follow conformai predictions with the decay exponents of the phenomenological scaling theory. Dynamical correlations in the critical state are in average logarithmically slow and their distribution shows multiscaling character. In the Griffiths phase, which is an extended part of the off-critical region, average autocorrelations have a power-law form with a nonuniversal decay exponent, which is analytically calculated. We note on extensions of our work to the random antiferromagnetic XXZ chain and to higher dimensions.

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

Pages (from-to) | 11552-11568 |

Number of pages | 17 |

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

Volume | 61 |

Issue number | 17 |

Publication status | Published - 2000 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

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

*61*(17), 11552-11568.

**Random antiferromagnetic quantum spin chains : Exact results from scaling of rare regions.** / Iglói, F.; Juhász, Róbert; Rieger, Heiko.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 61, no. 17, pp. 11552-11568.

}

TY - JOUR

T1 - Random antiferromagnetic quantum spin chains

T2 - Exact results from scaling of rare regions

AU - Iglói, F.

AU - Juhász, Róbert

AU - Rieger, Heiko

PY - 2000

Y1 - 2000

N2 - We study XY and dimerized XX spin-1/2 chains with random exchange couplings by analytical and numerical methods and scaling considerations. We extend previous investigations to dynamical properties, to surface quantities, and operator profiles, and give a detailed analysis of the Griffiths phase. We present a phenomenological scaling theory of average quantities based on the scaling properties of rare regions, in which the distribution of the couplings follows a surviving random-walk character. Using this theory we have obtained the complete set of critical decay exponents of the random XY and XX models, both in the volume and at the surface. The scaling results are confirmed by numerical calculations based on a mapping to free fermions, which then lead to an exact correspondence with directed walks. The numerically calculated critical operator profiles on large finite systems (L≤512) are found to follow conformai predictions with the decay exponents of the phenomenological scaling theory. Dynamical correlations in the critical state are in average logarithmically slow and their distribution shows multiscaling character. In the Griffiths phase, which is an extended part of the off-critical region, average autocorrelations have a power-law form with a nonuniversal decay exponent, which is analytically calculated. We note on extensions of our work to the random antiferromagnetic XXZ chain and to higher dimensions.

AB - We study XY and dimerized XX spin-1/2 chains with random exchange couplings by analytical and numerical methods and scaling considerations. We extend previous investigations to dynamical properties, to surface quantities, and operator profiles, and give a detailed analysis of the Griffiths phase. We present a phenomenological scaling theory of average quantities based on the scaling properties of rare regions, in which the distribution of the couplings follows a surviving random-walk character. Using this theory we have obtained the complete set of critical decay exponents of the random XY and XX models, both in the volume and at the surface. The scaling results are confirmed by numerical calculations based on a mapping to free fermions, which then lead to an exact correspondence with directed walks. The numerically calculated critical operator profiles on large finite systems (L≤512) are found to follow conformai predictions with the decay exponents of the phenomenological scaling theory. Dynamical correlations in the critical state are in average logarithmically slow and their distribution shows multiscaling character. In the Griffiths phase, which is an extended part of the off-critical region, average autocorrelations have a power-law form with a nonuniversal decay exponent, which is analytically calculated. We note on extensions of our work to the random antiferromagnetic XXZ chain and to higher dimensions.

UR - http://www.scopus.com/inward/record.url?scp=0001485158&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001485158&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001485158

VL - 61

SP - 11552

EP - 11568

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 17

ER -