### Abstract

We consider random extended surface perturbations in the transverse field Ising model decaying as a power of the distance from the surface towards a pure bulk system. The decay may be linked either to the evolution of the couplings or to their probabilities. Using scaling arguments, we develop a relevance-irrelevance criterion for such perturbations. We study the probability distribution of the surface magnetization, its average and typical critical behaviour for marginal and relevant perturbations. According to analytical results, the surface magnetization follows a log-normal distribution and both the average and typical critical behaviours are characterized by power-law singularities with continuously varying exponents in the marginal case and essential singularities in the relevant case. For enhanced average local couplings, the transition becomes first order with a nonvanishing critical surface magnetization. This occurs above a positive threshold value of the perturbation amplitude in the marginal case.

Original language | English |
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Pages (from-to) | 3907-3918 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 32 |

Issue number | 21 |

DOIs | |

Publication status | Published - May 28 1999 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*32*(21), 3907-3918. https://doi.org/10.1088/0305-4470/32/21/304

**Extended surface disorder in the quantum Ising chain.** / Turban, L.; Karevski, D.; Iglói, F.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 32, no. 21, pp. 3907-3918. https://doi.org/10.1088/0305-4470/32/21/304

}

TY - JOUR

T1 - Extended surface disorder in the quantum Ising chain

AU - Turban, L.

AU - Karevski, D.

AU - Iglói, F.

PY - 1999/5/28

Y1 - 1999/5/28

N2 - We consider random extended surface perturbations in the transverse field Ising model decaying as a power of the distance from the surface towards a pure bulk system. The decay may be linked either to the evolution of the couplings or to their probabilities. Using scaling arguments, we develop a relevance-irrelevance criterion for such perturbations. We study the probability distribution of the surface magnetization, its average and typical critical behaviour for marginal and relevant perturbations. According to analytical results, the surface magnetization follows a log-normal distribution and both the average and typical critical behaviours are characterized by power-law singularities with continuously varying exponents in the marginal case and essential singularities in the relevant case. For enhanced average local couplings, the transition becomes first order with a nonvanishing critical surface magnetization. This occurs above a positive threshold value of the perturbation amplitude in the marginal case.

AB - We consider random extended surface perturbations in the transverse field Ising model decaying as a power of the distance from the surface towards a pure bulk system. The decay may be linked either to the evolution of the couplings or to their probabilities. Using scaling arguments, we develop a relevance-irrelevance criterion for such perturbations. We study the probability distribution of the surface magnetization, its average and typical critical behaviour for marginal and relevant perturbations. According to analytical results, the surface magnetization follows a log-normal distribution and both the average and typical critical behaviours are characterized by power-law singularities with continuously varying exponents in the marginal case and essential singularities in the relevant case. For enhanced average local couplings, the transition becomes first order with a nonvanishing critical surface magnetization. This occurs above a positive threshold value of the perturbation amplitude in the marginal case.

UR - http://www.scopus.com/inward/record.url?scp=0033612085&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033612085&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/32/21/304

DO - 10.1088/0305-4470/32/21/304

M3 - Article

VL - 32

SP - 3907

EP - 3918

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 21

ER -