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.
Handford, P., Perez-Reche, F.-J. and 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. Available from http://dx.doi.org/10.1088/1742-5468/2012/01/P01001