Spin Dynamics near the Magnetic Percolation Threshold

An inelastic neutron-scattering study of spin relaxation in the dilute, two-dimensional Ising antiferromagnet ${\mathrm{Rb}}_2{\mathrm{Co}}_c{\mathrm{Mg}}_{1-c}{\mathrm{F}}_4$ has been carried out for $c$ very close to the magnetic percolation threshold $c_p=0.593\mathrm{}$. The dynamical exponent $z$ relating the order-parameter relaxation rate to the magnetic correlation length is found to be ${2.4}_{-0.1\mathrm{}}^{+0.2\mathrm{}}$. It is argued that $z$ has this anomalously high value because of the fractal geometry of percolating networks.