### Abstract

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents ω > 0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as L ∼ (lnt)^{1/ω}. Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of ω, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities.

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

Pages (from-to) | 613-625 |

Number of pages | 13 |

Journal | European Physical Journal B |

Volume | 5 |

Issue number | 3 |

Publication status | Published - 1998 |

### Fingerprint

### Keywords

- 05.50.+q Lattice theory and statistics; Ising problems
- 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions
- 68.35.Rh Phase transitions and critical phenomena

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*European Physical Journal B*,

*5*(3), 613-625.

**Comparative study of the critical behavior in one-dimensional random and aperiodic environments.** / Iglói, F.; Karevski, D.; Rieger, H.

Research output: Contribution to journal › Article

*European Physical Journal B*, vol. 5, no. 3, pp. 613-625.

}

TY - JOUR

T1 - Comparative study of the critical behavior in one-dimensional random and aperiodic environments

AU - Iglói, F.

AU - Karevski, D.

AU - Rieger, H.

PY - 1998

Y1 - 1998

N2 - We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents ω > 0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as L ∼ (lnt)1/ω. Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of ω, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities.

AB - We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents ω > 0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as L ∼ (lnt)1/ω. Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of ω, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities.

KW - 05.50.+q Lattice theory and statistics; Ising problems

KW - 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions

KW - 68.35.Rh Phase transitions and critical phenomena

UR - http://www.scopus.com/inward/record.url?scp=0032292147&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032292147&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032292147

VL - 5

SP - 613

EP - 625

JO - Zeitschrift für Physik B Condensed Matter and Quanta

JF - Zeitschrift für Physik B Condensed Matter and Quanta

SN - 1434-6028

IS - 3

ER -