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.
|Journal||Journal of Statistical Mechanics: Theory and Experiment|
|Publication status||Published - Jan 2012|
- Barkhausen noise (theory)
- Exact results
- Correlation functions (theory)
- Critical exponents and amplitudes (theory)