Exact spin-spin correlation function for the zero-temperature   random-field Ising model
  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. 
T.P. Handford, F.J. Perez-Reche and S.N. Taraskin
cond-mat.stat-mech cond-mat.dis-nn