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