Spin Correlations near the Percolation Concentration in Two Dimensions

Abstract

Neutron scattering measurements in the dilute antiferromagnets ${\mathrm{Rb}}_2{\mathrm{Mn}}_c{\mathrm{Mg}}_{1-c}{\mathrm{F}}_4$ with $c=0.54\mathrm{} \mathrm{and} 0.57$ are presented; for this system the percolation limit is $c_p=0.59\mathrm{}$. Two-dimensional critical scattering is observed with inverse width $\xi$ and amplitude $\chi T$ which diverge as a function of $\frac{1}{T}$; the divergences cut off when $\xi$ exceeds the size of the larger clusters. A simple self-avoiding walk model accounts well for the observed $\xi$ vs $T$ behavior.