### Abstract

An exact expression for the spin-spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spinspin correlations and separated from the intrinsic topological length scale of the Bethe lattice is shown to diverge as a power law at the critical point. The critical exponents governing the behaviour of the correlation length are consistent with the mean-field values found for a hypercubic lattice with dimension greater than the upper critical dimension.

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

Article number | P01001 |

Number of pages | 21 |

Journal | Journal of statistical mechanics-Theory and experiment |

Volume | 2012 |

DOIs | |

Publication status | Published - Jan 2012 |

### Cite this

*Journal of statistical mechanics-Theory and experiment*,

*2012*, [P01001]. https://doi.org/10.1088/1742-5468/2012/01/P01001

**Exact spin-spin correlation function for the zero-temperature random-field Ising model.** / Handford, T. P.; Perez-Reche, F. J.; Taraskin, S. N.

Research output: Contribution to journal › Article

*Journal of statistical mechanics-Theory and experiment*, vol. 2012, P01001. https://doi.org/10.1088/1742-5468/2012/01/P01001

}

TY - JOUR

T1 - Exact spin-spin correlation function for the zero-temperature random-field Ising model

AU - Handford, T. P.

AU - Perez-Reche, F. J.

AU - Taraskin, S. N.

PY - 2012/1

Y1 - 2012/1

N2 - An exact expression for the spin-spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spinspin correlations and separated from the intrinsic topological length scale of the Bethe lattice is shown to diverge as a power law at the critical point. The critical exponents governing the behaviour of the correlation length are consistent with the mean-field values found for a hypercubic lattice with dimension greater than the upper critical dimension.

AB - An exact expression for the spin-spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spinspin correlations and separated from the intrinsic topological length scale of the Bethe lattice is shown to diverge as a power law at the critical point. The critical exponents governing the behaviour of the correlation length are consistent with the mean-field values found for a hypercubic lattice with dimension greater than the upper critical dimension.

U2 - 10.1088/1742-5468/2012/01/P01001

DO - 10.1088/1742-5468/2012/01/P01001

M3 - Article

VL - 2012

JO - Journal of statistical mechanics-Theory and experiment

JF - Journal of statistical mechanics-Theory and experiment

SN - 1742-5468

M1 - P01001

ER -