### Abstract

We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents β ≈ 3.6 and β_{1} ≈ 4.1 in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent α ≈ -3.1. The samples reduced critical temperature t_{c} = T^{av}_{c} - T_{c} has a power law distribution P(t_{c}) ∼ t^{ω}_{c} and we show that the difference between the values of the critical exponents in the pure and in the random system is just ω ≈ 3.1. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.

Original language | English |
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Pages (from-to) | 5193-5202 |

Number of pages | 10 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 31 |

Issue number | 23 |

DOIs | |

Publication status | Published - Jun 12 1998 |

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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*,

*31*(23), 5193-5202. https://doi.org/10.1088/0305-4470/31/23/003

**The McCoy-Wu model in the mean-field approximation.** / Berche, Bertrand; Berche, Pierre Emmanuel; Iglói, F.; Palágyi, Gábor.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 31, no. 23, pp. 5193-5202. https://doi.org/10.1088/0305-4470/31/23/003

}

TY - JOUR

T1 - The McCoy-Wu model in the mean-field approximation

AU - Berche, Bertrand

AU - Berche, Pierre Emmanuel

AU - Iglói, F.

AU - Palágyi, Gábor

PY - 1998/6/12

Y1 - 1998/6/12

N2 - We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents β ≈ 3.6 and β1 ≈ 4.1 in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent α ≈ -3.1. The samples reduced critical temperature tc = Tavc - Tc has a power law distribution P(tc) ∼ tωc and we show that the difference between the values of the critical exponents in the pure and in the random system is just ω ≈ 3.1. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.

AB - We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents β ≈ 3.6 and β1 ≈ 4.1 in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent α ≈ -3.1. The samples reduced critical temperature tc = Tavc - Tc has a power law distribution P(tc) ∼ tωc and we show that the difference between the values of the critical exponents in the pure and in the random system is just ω ≈ 3.1. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.

UR - http://www.scopus.com/inward/record.url?scp=0032510931&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032510931&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/31/23/003

DO - 10.1088/0305-4470/31/23/003

M3 - Article

AN - SCOPUS:0032510931

VL - 31

SP - 5193

EP - 5202

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 23

ER -