### 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 spin–spin 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 |
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Article number | P01001 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2012 |

DOIs | |

Publication status | Published - Jan 2012 |

Externally published | Yes |

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## Cite this

Handford, P., Perez-Reche, F. J., & Taraskin, S. N. (2012). Exact spin–spin correlation function for the zero-temperature random-field Ising model.

*Journal of Statistical Mechanics: Theory and Experiment*,*2012*, [P01001]. https://doi.org/10.1088/1742-5468/2012/01/P01001